diff --git a/linear_algebra/system_of_linear_equations_mod_2/checker.cpp b/linear_algebra/system_of_linear_equations_mod_2/checker.cpp
new file mode 100644
index 00000000..031dd830
--- /dev/null
+++ b/linear_algebra/system_of_linear_equations_mod_2/checker.cpp
@@ -0,0 +1,89 @@
+#include <algorithm>
+#include <vector>
+#include <string>
+#include <bitset>
+#include "testlib.h"
+
+using namespace std;
+using BS = bitset<4096>;
+
+int N, M;
+BS A[4096];
+BS b;
+
+BS evaluate(BS x) {
+  BS y;
+  for (int i = 0; i < N; ++i) {
+    int cnt = (x & A[i]).count();
+    y[i] = cnt % 2;
+  }
+  return y;
+}
+
+int matrix_rank(vector<BS> a) {
+  int N = a.size();
+  int rk = 0;
+  for (int j = 0; j < M; ++j) {
+    if (rk == N) break;
+    if (!a[rk][j]) {
+      for (int i = rk + 1; i < N; ++i) {
+        if (a[i][j]) {
+          swap(a[rk], a[i]);
+          break;
+        }
+      }
+    }
+    if (!a[rk][j]) continue;
+    for (int i = rk + 1; i < N; ++i) {
+      if (a[i][j]) { a[i] ^= a[rk]; }
+    }
+    ++rk;
+  }
+  return rk;
+}
+
+int get_rank(InStream& stream) {
+  int r = stream.readInt(-1, M);
+  if (r == -1) return -1;
+  vector<BS> mat;
+
+  for (int k = 0; k < r + 1; ++k) {
+    string S = stream.readToken();
+    stream.ensure(int(S.size()) == M);
+    for (auto& ch: S) stream.ensure(ch == '0' || ch == '1');
+    BS x;
+    for (int j = 0; j < M; ++j) x[j] = (S[j] - '0');
+    BS y = evaluate(x);
+    if (k == 0) {
+      for (int i = 0; i < N; ++i) { stream.ensure(y[i] == b[i]); }
+    } else {
+      for (int i = 0; i < N; ++i) { stream.ensure(y[i] == false); }
+      mat.emplace_back(x);
+    }
+  }
+  stream.ensure(matrix_rank(mat) == r);
+  return r;
+}
+
+int main(int argc, char* argv[]) {
+  registerTestlibCmd(argc, argv);
+  // read input
+  N = inf.readInt();
+  M = inf.readInt();
+  for (int i = 0; i < N; ++i) {
+    string S = inf.readToken();
+    for (int j = 0; j < M; ++j) A[i][j] = (S[j] - '0');
+  }
+  string S = inf.readToken();
+  for (int i = 0; i < N; ++i) b[i] = (S[i] - '0');
+
+  int k_ans = get_rank(ans);
+  int k_ouf = get_rank(ouf);
+
+  if (k_ans == -1 && k_ouf == -1) { quitf(_ok, "OK No solution"); }
+  if (k_ans != -1 && k_ouf == -1) { quitf(_wa, "WA you cannot find solution"); }
+  if (k_ans == -1 && k_ouf != -1) { quitf(_fail, "Judge cannot find solution"); }
+  if (k_ans > k_ouf) { quitf(_wa, "There are more solutions"); }
+  if (k_ans < k_ouf) { quitf(_fail, "What happened?"); }
+  quitf(_ok, "OK");
+}
diff --git a/linear_algebra/system_of_linear_equations_mod_2/gen/base.hpp b/linear_algebra/system_of_linear_equations_mod_2/gen/base.hpp
new file mode 100644
index 00000000..6cc3341b
--- /dev/null
+++ b/linear_algebra/system_of_linear_equations_mod_2/gen/base.hpp
@@ -0,0 +1,73 @@
+#include <bitset>
+#include <vector>
+#include "random.h"
+
+using namespace std;
+using BS = bitset<4096>;
+
+void out(int n, int m, vector<BS> A, BS b) {
+  auto out_BS = [&](int n, BS x) -> void {
+    string S(n, '?');
+    for (int i = 0; i < n; ++i) S[i] = (x[i] ? '1' : '0');
+    printf("%s\n", S.c_str());
+  };
+  printf("%d %d\n", n, m);
+  for (int i = 0; i < n; ++i) out_BS(m, A[i]);
+  out_BS(n, b);
+}
+
+void gen_yes(int n, int m, int r, Random &gen) {
+  assert(r <= m && r <= n);
+  vector<BS> a(n);
+  for (int i = 0; i < r; ++i) {
+    for (int j = 0; j < m; ++j) { a[i][j] = gen.uniform_bool(); }
+  }
+  for (int i = r; i < n; ++i) {
+    for (int k = 0; k < r; ++k) {
+      if (gen.uniform_bool()) a[i] ^= a[k];
+    }
+  }
+  // shuffle
+  gen.shuffle(a.begin(), a.end());
+
+  BS x;
+  for (int i = 0; i < m; ++i) x[i] = gen.uniform_bool();
+  BS y;
+  for (int i = 0; i < n; ++i) { y[i] = (a[i] & x).count() % 2; }
+  out(n, m, a, y);
+}
+
+void gen_no(int n, int m, int r, Random &gen) {
+  assert(r <= m && r < n);
+  vector<BS> a(n);
+  for (int i = 0; i < r; ++i) {
+    for (int j = 0; j < m; ++j) { a[i][j] = gen.uniform_bool(); }
+  }
+
+  BS y;
+  for (int i = 0; i < n; ++i) { y[i] = gen.uniform_bool(); }
+  // at least one 1
+  y[gen.uniform<int>(r, n - 1)] = 1;
+
+  for (int i = r; i < n; ++i) {
+    for (int k = 0; k < r; ++k) {
+      if (gen.uniform_bool()) {
+        a[i] ^= a[k];
+        y[i] = y[i] ^ y[k];
+      }
+    }
+  }
+
+  // shuffle
+  vector<int> new_idx(n);
+  for (int i = 0; i < n; ++i) new_idx[i] = i;
+  gen.shuffle(new_idx.begin(), new_idx.end());
+  vector<BS> new_a(n);
+  BS new_y;
+  for (int i = 0; i < n; ++i) {
+    new_a[new_idx[i]] = a[i];
+    new_y[new_idx[i]] = y[i];
+  }
+
+  out(n, m, new_a, new_y);
+}
diff --git a/linear_algebra/system_of_linear_equations_mod_2/gen/example_00.in b/linear_algebra/system_of_linear_equations_mod_2/gen/example_00.in
new file mode 100644
index 00000000..867988bc
--- /dev/null
+++ b/linear_algebra/system_of_linear_equations_mod_2/gen/example_00.in
@@ -0,0 +1,5 @@
+3 3
+101
+011
+110
+011
diff --git a/linear_algebra/system_of_linear_equations_mod_2/gen/example_01.in b/linear_algebra/system_of_linear_equations_mod_2/gen/example_01.in
new file mode 100644
index 00000000..c4700cfb
--- /dev/null
+++ b/linear_algebra/system_of_linear_equations_mod_2/gen/example_01.in
@@ -0,0 +1,5 @@
+3 3
+101
+011
+110
+111
diff --git a/linear_algebra/system_of_linear_equations_mod_2/gen/example_02.in b/linear_algebra/system_of_linear_equations_mod_2/gen/example_02.in
new file mode 100644
index 00000000..83755b9a
--- /dev/null
+++ b/linear_algebra/system_of_linear_equations_mod_2/gen/example_02.in
@@ -0,0 +1,3 @@
+1 3
+111
+1
diff --git a/linear_algebra/system_of_linear_equations_mod_2/gen/max_lowrank.cpp b/linear_algebra/system_of_linear_equations_mod_2/gen/max_lowrank.cpp
new file mode 100644
index 00000000..139efc80
--- /dev/null
+++ b/linear_algebra/system_of_linear_equations_mod_2/gen/max_lowrank.cpp
@@ -0,0 +1,20 @@
+#include <iostream>
+#include "random.h"
+#include "../params.h"
+#include "base.hpp"
+
+using namespace std;
+
+int main(int, char* argv[]) {
+  long long seed = atoll(argv[1]);
+  auto gen = Random(seed);
+
+  int rs[] = {1, 10, 100, 1000, 4000};
+
+  int n = N_MAX;
+  int m = M_MAX;
+  int r = rs[seed % 5];
+  if (seed % 2 == 0) gen_yes(n, m, r, gen);
+  if (seed % 2 == 1) gen_no(n, m, r, gen);
+  return 0;
+}
diff --git a/linear_algebra/system_of_linear_equations_mod_2/gen/max_random.cpp b/linear_algebra/system_of_linear_equations_mod_2/gen/max_random.cpp
new file mode 100644
index 00000000..07f66d2b
--- /dev/null
+++ b/linear_algebra/system_of_linear_equations_mod_2/gen/max_random.cpp
@@ -0,0 +1,27 @@
+#include <iostream>
+#include "random.h"
+#include "../params.h"
+
+using namespace std;
+
+int main(int, char* argv[]) {
+  long long seed = atoll(argv[1]);
+  auto gen = Random(seed);
+
+  int n = N_MAX;
+  int m = M_MAX;
+  auto random_01_str = [&](int n) -> string {
+    string S(n, '?');
+    for (int i = 0; i < n; ++i) S[i] = '0' + gen.uniform(0, 1);
+    return S;
+  };
+
+  printf("%d %d\n", n, m);
+  for (int i = 0; i < n; i++) {
+    string S = random_01_str(m);
+    printf("%s\n", S.c_str());
+  }
+  string S = random_01_str(n);
+  printf("%s\n", S.c_str());
+  return 0;
+}
diff --git a/linear_algebra/system_of_linear_equations_mod_2/gen/max_small.cpp b/linear_algebra/system_of_linear_equations_mod_2/gen/max_small.cpp
new file mode 100644
index 00000000..c6767995
--- /dev/null
+++ b/linear_algebra/system_of_linear_equations_mod_2/gen/max_small.cpp
@@ -0,0 +1,18 @@
+#include <iostream>
+#include "random.h"
+#include "../params.h"
+#include "base.hpp"
+
+using namespace std;
+
+int main(int, char* argv[]) {
+  long long seed = atoll(argv[1]);
+  auto gen = Random(seed);
+
+  int n = N_MAX;
+  int m = gen.uniform<int>(2, 10);
+  int r = gen.uniform<int>(1, min(n, m) - 1);
+  if (seed % 2 == 0) gen_yes(n, m, r, gen);
+  if (seed % 2 == 1) gen_no(n, m, r, gen);
+  return 0;
+}
diff --git a/linear_algebra/system_of_linear_equations_mod_2/gen/random.cpp b/linear_algebra/system_of_linear_equations_mod_2/gen/random.cpp
new file mode 100644
index 00000000..75c041b7
--- /dev/null
+++ b/linear_algebra/system_of_linear_equations_mod_2/gen/random.cpp
@@ -0,0 +1,27 @@
+#include <iostream>
+#include "random.h"
+#include "../params.h"
+
+using namespace std;
+
+int main(int, char* argv[]) {
+  long long seed = atoll(argv[1]);
+  auto gen = Random(seed);
+
+  int n = gen.uniform<int>(1, N_MAX);
+  int m = gen.uniform<int>(1, M_MAX);
+  auto random_01_str = [&](int n) -> string {
+    string S(n, '?');
+    for (int i = 0; i < n; ++i) S[i] = '0' + gen.uniform(0, 1);
+    return S;
+  };
+
+  printf("%d %d\n", n, m);
+  for (int i = 0; i < n; i++) {
+    string S = random_01_str(m);
+    printf("%s\n", S.c_str());
+  }
+  string S = random_01_str(n);
+  printf("%s\n", S.c_str());
+  return 0;
+}
diff --git a/linear_algebra/system_of_linear_equations_mod_2/gen/small_max.cpp b/linear_algebra/system_of_linear_equations_mod_2/gen/small_max.cpp
new file mode 100644
index 00000000..a06e8e40
--- /dev/null
+++ b/linear_algebra/system_of_linear_equations_mod_2/gen/small_max.cpp
@@ -0,0 +1,18 @@
+#include <iostream>
+#include "random.h"
+#include "../params.h"
+#include "base.hpp"
+
+using namespace std;
+
+int main(int, char* argv[]) {
+  long long seed = atoll(argv[1]);
+  auto gen = Random(seed);
+
+  int n = gen.uniform<int>(2, 10);
+  int m = M_MAX;
+  int r = gen.uniform<int>(1, min(n, m) - 1);
+  if (seed % 2 == 0) gen_yes(n, m, r, gen);
+  if (seed % 2 == 1) gen_no(n, m, r, gen);
+  return 0;
+}
diff --git a/linear_algebra/system_of_linear_equations_mod_2/gen/small_random.cpp b/linear_algebra/system_of_linear_equations_mod_2/gen/small_random.cpp
new file mode 100644
index 00000000..076ff328
--- /dev/null
+++ b/linear_algebra/system_of_linear_equations_mod_2/gen/small_random.cpp
@@ -0,0 +1,27 @@
+#include <iostream>
+#include "random.h"
+#include "../params.h"
+
+using namespace std;
+
+int main(int, char* argv[]) {
+  long long seed = atoll(argv[1]);
+  auto gen = Random(seed);
+
+  int n = gen.uniform<int>(1, 3);
+  int m = gen.uniform<int>(1, 3);
+  auto random_01_str = [&](int n) -> string {
+    string S(n, '?');
+    for (int i = 0; i < n; ++i) S[i] = '0' + gen.uniform(0, 1);
+    return S;
+  };
+
+  printf("%d %d\n", n, m);
+  for (int i = 0; i < n; i++) {
+    string S = random_01_str(m);
+    printf("%s\n", S.c_str());
+  }
+  string S = random_01_str(n);
+  printf("%s\n", S.c_str());
+  return 0;
+}
diff --git a/linear_algebra/system_of_linear_equations_mod_2/gen/smallest_00.in b/linear_algebra/system_of_linear_equations_mod_2/gen/smallest_00.in
new file mode 100644
index 00000000..8550cfd6
--- /dev/null
+++ b/linear_algebra/system_of_linear_equations_mod_2/gen/smallest_00.in
@@ -0,0 +1,3 @@
+1 1
+0
+0
diff --git a/linear_algebra/system_of_linear_equations_mod_2/gen/smallest_01.in b/linear_algebra/system_of_linear_equations_mod_2/gen/smallest_01.in
new file mode 100644
index 00000000..82e1ed21
--- /dev/null
+++ b/linear_algebra/system_of_linear_equations_mod_2/gen/smallest_01.in
@@ -0,0 +1,3 @@
+1 1
+0
+1
diff --git a/linear_algebra/system_of_linear_equations_mod_2/gen/smallest_02.in b/linear_algebra/system_of_linear_equations_mod_2/gen/smallest_02.in
new file mode 100644
index 00000000..56ebc3a9
--- /dev/null
+++ b/linear_algebra/system_of_linear_equations_mod_2/gen/smallest_02.in
@@ -0,0 +1,3 @@
+1 1
+1
+0
diff --git a/linear_algebra/system_of_linear_equations_mod_2/gen/smallest_03.in b/linear_algebra/system_of_linear_equations_mod_2/gen/smallest_03.in
new file mode 100644
index 00000000..fa06f247
--- /dev/null
+++ b/linear_algebra/system_of_linear_equations_mod_2/gen/smallest_03.in
@@ -0,0 +1,3 @@
+1 1
+1
+1
diff --git a/linear_algebra/system_of_linear_equations_mod_2/hash.json b/linear_algebra/system_of_linear_equations_mod_2/hash.json
new file mode 100644
index 00000000..207ddd3a
--- /dev/null
+++ b/linear_algebra/system_of_linear_equations_mod_2/hash.json
@@ -0,0 +1,74 @@
+{
+  "example_00.in": "6063634b3c8f31aaf3078a8c22c3cdd8b53e4050846df4abd9d8f80cd43a7ef7",
+  "example_00.out": "e5ba645c12ed5697234f5d87e0cee43b0bd05dc5c8dd5026773b9bbc4c84a820",
+  "example_01.in": "fd2399647e31fcecbd55921de8aac02c20867fb3fa06c84abeffd4de72370b23",
+  "example_01.out": "ee3aa64bb94a50845d5024cd4bd20202a4567aed5cd5328c0d97e9920775fc28",
+  "example_02.in": "cdb150eaa586f422a1e0429b7189b4c3818edda13433e81a51e326e4265fe037",
+  "example_02.out": "2a7863cc0aeace6e8a08f3c5c2f564c685367bc60c65b1a65b211e6f21a28204",
+  "max_lowrank_00.in": "6638c04e8e68603cf0b5793646e5cd97da74845a2e698fcbe4926153e0b034f7",
+  "max_lowrank_00.out": "1cbff4f7984fa485b4bafa2e7cb87760c081628850b437fa2ee6db792bdaa41f",
+  "max_lowrank_01.in": "1786aa087f73e997aa44d97d6fba6ed00105968c9d630c9374f316e43f91f6fb",
+  "max_lowrank_01.out": "ee3aa64bb94a50845d5024cd4bd20202a4567aed5cd5328c0d97e9920775fc28",
+  "max_lowrank_02.in": "bbe5a65f8b0b606dcb1f30e52a446f57b9bdd14fee234e58c2187de7fe0b5544",
+  "max_lowrank_02.out": "95c6e77f883f3251cf7086e9974ae5dacf90a4460971735c0de7828efb72ce4f",
+  "max_lowrank_03.in": "aab930335a5a484401015450290e5f2f37a08b6a2d09cde429ae659ac77c1789",
+  "max_lowrank_03.out": "ee3aa64bb94a50845d5024cd4bd20202a4567aed5cd5328c0d97e9920775fc28",
+  "max_lowrank_04.in": "8ee5123b7f3cb3a852d83ff13b9f47badb42f21b322d10ead350c32005854b52",
+  "max_lowrank_04.out": "c6dde9b67e9ede353faaff3093c1a3889f058f6a37802a5fff5607dd64a9af6e",
+  "max_lowrank_05.in": "3d4e7b300e10337c68a607944df0980d73f0919191b86fd8d15693be3a446092",
+  "max_lowrank_05.out": "ee3aa64bb94a50845d5024cd4bd20202a4567aed5cd5328c0d97e9920775fc28",
+  "max_lowrank_06.in": "119dcae58eb863729ac38fa8e815bcba0dc4b790e110fd1dd787b9720b627a4a",
+  "max_lowrank_06.out": "1092c7fc6c2d6a0f0d35bd04a776e906b8ff376015c5d912380d93fa81ead70a",
+  "max_lowrank_07.in": "a70ce08bda2a9f2e1b493ecc7600a6c54f65eba7de515c76a2573a1d31f728ff",
+  "max_lowrank_07.out": "ee3aa64bb94a50845d5024cd4bd20202a4567aed5cd5328c0d97e9920775fc28",
+  "max_lowrank_08.in": "a0c42ec11aae679d3fc0a57eaa7864c0a0b26c156daf8f1f32192ae12292cda7",
+  "max_lowrank_08.out": "870d275ec5452b46a76b780214dd72aa6139be340f09fd39b6666b8ff5395e27",
+  "max_lowrank_09.in": "b219971c910a4e9d16146761975ba599dd6671fb565262bc61f5d1006e304b51",
+  "max_lowrank_09.out": "ee3aa64bb94a50845d5024cd4bd20202a4567aed5cd5328c0d97e9920775fc28",
+  "max_random_00.in": "e6e5a5f028dd1e1ac24bd8cae64c67b022c2da23c667e545bc8bdb30dbf382c3",
+  "max_random_00.out": "ee3aa64bb94a50845d5024cd4bd20202a4567aed5cd5328c0d97e9920775fc28",
+  "max_random_01.in": "e4eab8c7c8920d14b4db35b38ca8e50e6c6fb35ec13f0fdcc3a25e1d58e3188a",
+  "max_random_01.out": "eebb9700465e9fd322f5916a3e3a16082deac8ee7bf561a977c6483aa29d61d6",
+  "max_random_02.in": "10ba78d1ab65588fd20c4b157b96859e87a6f49031500aafbc0e54421086e1c1",
+  "max_random_02.out": "87830da28ca0340dd748484b4ed8e87d7a392412cbde7ac390be147255757769",
+  "max_random_03.in": "9a2dacdc0a7b53adeea8cb59a44906b488a0aa76b82e957e0317c56afde9c2ec",
+  "max_random_03.out": "ee3aa64bb94a50845d5024cd4bd20202a4567aed5cd5328c0d97e9920775fc28",
+  "max_random_04.in": "0bb65fc99cb2a29a0b82e11a9502b0ecc50e8d5b22904fa998cd66b593a29b61",
+  "max_random_04.out": "a751f1e4acb5cfc16d7daabcc4c6073b675dd9e20e8094e9cd8e903a83e7060e",
+  "max_small_00.in": "423f3ba9fd2b89970fd099f1a98e78add8c8702f9996662a375417cbf98a1005",
+  "max_small_00.out": "2b3fcb7b98f30fd92c50d331255c08440ed9c423a5527f7caf80018139f6a07c",
+  "max_small_01.in": "37bbd1cb74cc6b66d8afbdf3f6fe34ee87d48ea80d9598cd9ccc6f6b41a6d504",
+  "max_small_01.out": "ee3aa64bb94a50845d5024cd4bd20202a4567aed5cd5328c0d97e9920775fc28",
+  "random_00.in": "611c05258c9bed06038e9e667a33f77ce649ee071327c68e4e302e93428d1cfc",
+  "random_00.out": "527bee4215a969e7872cef01ed103212834fa4bf4128acd5de4ef21794a9510a",
+  "random_01.in": "b577ffaa423711baf18e534360f5ce0e25a51c4e5eda44962138778abe6b82c7",
+  "random_01.out": "3af7b14001f9ebf2361ce50909487183d168cecefe308892cb8e67cedc95325f",
+  "random_02.in": "ecb7e49a76a27b5bfe45673cb205655c1a5a21b10740a2b556b2d35e1e14cf27",
+  "random_02.out": "5e01a5dea71a66d368078237a6c6b4f6006424ad9c2b0ac7329d8175e58fa4c7",
+  "random_03.in": "fe3cc828676cd6ffb0a1266fbf99278d194981540b776d5df239454c30248f07",
+  "random_03.out": "ee3aa64bb94a50845d5024cd4bd20202a4567aed5cd5328c0d97e9920775fc28",
+  "random_04.in": "af3c71dd2b28cfbc25b8de3f29760b9867f4ee1019e6660959c87e8464f81aac",
+  "random_04.out": "ee3aa64bb94a50845d5024cd4bd20202a4567aed5cd5328c0d97e9920775fc28",
+  "small_max_00.in": "89ea26b22a2432afa0ada82090b1608e90521dbbbc921ab16e9f59ff685ae8cb",
+  "small_max_00.out": "bfbfd40999eb4e2006d88888007c749b982dd1a6398e64d77fc5f863d19b6060",
+  "small_max_01.in": "f5574faa4a2954961a68a82c298699c4d925da7e5d4d51a633fa8dd9b3e355d7",
+  "small_max_01.out": "ee3aa64bb94a50845d5024cd4bd20202a4567aed5cd5328c0d97e9920775fc28",
+  "small_random_00.in": "63f62781d1b4d9da4e62c279b3fa00adf84b016a817f0c83020c90bdffe5c492",
+  "small_random_00.out": "e30db10f9e3d4cb0abc5e29aeebbeaccedb49322abf4905f0de9cde81cc69bf4",
+  "small_random_01.in": "431375d2119248e201ee4bc87af17b19a60ec90859cdb7b00a1658cd9ddd6f04",
+  "small_random_01.out": "fbd3659d33448e458de8fd2972b27a061ddd037a1dd08f2e5e88d27862c0d5d7",
+  "small_random_02.in": "0c576d991bb5a27c47cbbdd5e5812d1cc91f18a3ca7ccde4d76ac7cf33b44e72",
+  "small_random_02.out": "ee3aa64bb94a50845d5024cd4bd20202a4567aed5cd5328c0d97e9920775fc28",
+  "small_random_03.in": "9142de3ca7f55a060928c24bf06a2bd8d78274a1aef486291cac3ca996353f36",
+  "small_random_03.out": "feb8513038ebe210da5e78db6025f2cc021956be75402b9f364ea17569f2e8f0",
+  "small_random_04.in": "23fb973368a17ad6b34c11df9eccd75362a91679050977591187372215f70fa6",
+  "small_random_04.out": "44bc3f637732558aeee7211e96d5b372fcdd4a441a95aec1fc183677fc41f55c",
+  "smallest_00.in": "e143ec05631e8515c810286dceeeaa93d4d433bd83ed980079e7da1958c8a17e",
+  "smallest_00.out": "a714acf0208a1a2e55902965ae577dcc30aa50e1fb1ba16a525e7f5cca653428",
+  "smallest_01.in": "1bf5777e213ac99383a7b880f4508fb256a7fe85aa466378b375908f653d489e",
+  "smallest_01.out": "ee3aa64bb94a50845d5024cd4bd20202a4567aed5cd5328c0d97e9920775fc28",
+  "smallest_02.in": "46964811c1e5d970fb6adebde76da0dcf1d0954921d349575538d34b90bfee86",
+  "smallest_02.out": "52f96c26a39ed25108a6db43d6e11c6051eba8a498a5baab1891adfa7ac7c262",
+  "smallest_03.in": "8b88a21ef03528d1b1eb90b24e9a05cb51fc2f935555f94f3999f2f6467ddf0f",
+  "smallest_03.out": "82c1315e6c757f33c4a77ca58b2a184f5a88614470c05ec77f3d28918db6b8ae"
+}
\ No newline at end of file
diff --git a/linear_algebra/system_of_linear_equations_mod_2/info.toml b/linear_algebra/system_of_linear_equations_mod_2/info.toml
new file mode 100644
index 00000000..a183b699
--- /dev/null
+++ b/linear_algebra/system_of_linear_equations_mod_2/info.toml
@@ -0,0 +1,32 @@
+title = 'System of Linear Equations (Mod 2)'
+timelimit = 5.0
+forum = "https://github.com/yosupo06/library-checker-problems/issues/896"
+
+[[tests]]
+    name = "example.in"
+    number = 3
+[[tests]]
+    name = "smallest.in"
+    number = 4
+[[tests]]
+    name = "small_random.cpp"
+    number = 5
+[[tests]]
+    name = "random.cpp"
+    number = 5
+[[tests]]
+    name = "max_random.cpp"
+    number = 5
+[[tests]]
+    name = "max_small.cpp"
+    number = 2
+[[tests]]
+    name = "small_max.cpp"
+    number = 2
+[[tests]]
+    name = "max_lowrank.cpp"
+    number = 10
+
+[params]
+    N_MAX = 4096
+    M_MAX = 4096
diff --git a/linear_algebra/system_of_linear_equations_mod_2/sol/correct.cpp b/linear_algebra/system_of_linear_equations_mod_2/sol/correct.cpp
new file mode 100644
index 00000000..04417fd3
--- /dev/null
+++ b/linear_algebra/system_of_linear_equations_mod_2/sol/correct.cpp
@@ -0,0 +1,193 @@
+#include <cstdlib>
+#include <cstdio>
+#include <vector>
+#include <bitset>
+#include <cassert>
+#include <tuple>
+#include <string>
+
+using namespace std;
+
+using ll = long long;
+using u32 = unsigned int;
+using u64 = unsigned long long;
+
+using pi = pair<ll, ll>;
+using vi = vector<ll>;
+template <class T>
+using vc = vector<T>;
+template <class T>
+using vvc = vector<vc<T>>;
+
+#define vv(type, name, h, ...) vector<vector<type>> name(h, vector<type>(__VA_ARGS__))
+
+#define FOR1(a) for (ll _ = 0; _ < ll(a); ++_)
+#define FOR2(i, a) for (ll i = 0; i < ll(a); ++i)
+#define FOR3(i, a, b) for (ll i = a; i < ll(b); ++i)
+#define FOR4(i, a, b, c) for (ll i = a; i < ll(b); i += (c))
+#define FOR1_R(a) for (ll i = (a)-1; i >= ll(0); --i)
+#define FOR2_R(i, a) for (ll i = (a)-1; i >= ll(0); --i)
+#define FOR3_R(i, a, b) for (ll i = (b)-1; i >= ll(a); --i)
+#define overload4(a, b, c, d, e, ...) e
+#define overload3(a, b, c, d, ...) d
+#define FOR(...) overload4(__VA_ARGS__, FOR4, FOR3, FOR2, FOR1)(__VA_ARGS__)
+#define FOR_R(...) overload3(__VA_ARGS__, FOR3_R, FOR2_R, FOR1_R)(__VA_ARGS__)
+
+#define all(x) x.begin(), x.end()
+#define len(x) ll(x.size())
+#define elif else if
+
+#define eb emplace_back
+#define mp make_pair
+#define mt make_tuple
+#define fi first
+#define se second
+
+int topbit(u64 x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
+int lowbit(u64 x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }
+
+template <typename T, typename U>
+T SUM(const vector<U> &A) {
+  T sm = 0;
+  for (auto &&a: A) sm += a;
+  return sm;
+}
+
+template <class T, class S>
+inline bool chmax(T &a, const S &b) {
+  return (a < b ? a = b, 1 : 0);
+}
+template <class T, class S>
+inline bool chmin(T &a, const S &b) {
+  return (a > b ? a = b, 1 : 0);
+}
+
+struct My_Bitset {
+  using T = My_Bitset;
+  int N;
+  vc<u64> dat;
+
+  // x で埋める
+  My_Bitset(int N = 0, int x = 0) : N(N) {
+    assert(x == 0 || x == 1);
+    u64 v = (x == 0 ? 0 : -1);
+    dat.assign((N + 63) >> 6, v);
+    if (N) dat.back() >>= (64 * len(dat) - N);
+  }
+
+  int size() { return N; }
+
+  class Proxy {
+  public:
+    Proxy(vc<u64> &d, int i) : dat(d), index(i) {}
+    operator bool() const { return (dat[index >> 6] >> (index & 63)) & 1; }
+
+    Proxy &operator=(u64 value) {
+      dat[index >> 6] &= ~(u64(1) << (index & 63));
+      dat[index >> 6] |= (value & 1) << (index & 63);
+      return *this;
+    }
+    void flip() {
+      dat[index >> 6] ^= (u64(1) << (index & 63)); // XOR to flip the bit
+    }
+
+  private:
+    vc<u64> &dat;
+    int index;
+  };
+
+  Proxy operator[](int i) { return Proxy(dat, i); }
+
+  T &operator^=(const T &p) {
+    assert(N == p.N);
+    FOR(i, len(dat)) dat[i] ^= p.dat[i];
+    return *this;
+  }
+  T operator^(const T &p) const { return T(*this) ^= p; }
+
+  static string TO_STR[256];
+  string to_string() const {
+    if (TO_STR[0].empty()) precompute();
+    string S;
+    for (auto &x: dat) { FOR(i, 8) S += TO_STR[(x >> (8 * i) & 255)]; }
+    S.resize(N);
+    return S;
+  }
+
+  static void precompute() {
+    FOR(s, 256) {
+      string x;
+      FOR(i, 8) x += '0' + (s >> i & 1);
+      TO_STR[s] = x;
+    }
+  }
+};
+string My_Bitset::TO_STR[256];
+
+vc<My_Bitset> solve_linear(int n, int m, vc<My_Bitset> A, My_Bitset b) {
+  using BS = My_Bitset;
+  assert(len(b) == n);
+  int rk = 0;
+  FOR(j, m) {
+    if (rk == n) break;
+    FOR(i, rk + 1, n) if (A[i][j]) {
+      swap(A[rk], A[i]);
+      if (b[rk] != b[i]) b[rk] = !b[rk], b[i] = !b[i];
+      break;
+    }
+    if (!A[rk][j]) continue;
+    FOR(i, n) if (i != rk) {
+      if (A[i][j]) { b[i] = b[i] ^ b[rk], A[i] = A[i] ^ A[rk]; }
+    }
+    ++rk;
+  }
+  FOR(i, rk, n) if (b[i]) return {};
+  vc<BS> res(1, BS(m));
+
+  vc<int> pivot(m, -1);
+  int p = 0;
+  FOR(i, rk) {
+    while (!A[i][p]) ++p;
+    res[0][p] = bool(b[i]), pivot[p] = i;
+  }
+  FOR(j, m) if (pivot[j] == -1) {
+    BS x(m);
+    x[j] = 1;
+    FOR(k, j) if (pivot[k] != -1 && A[pivot[k]][j]) x[k] = 1;
+    res.eb(x);
+  }
+  return res;
+}
+
+void solve() {
+  int N, M;
+  scanf("%d %d\n", &N, &M);
+  using BS = My_Bitset;
+  auto get = [&](int n) -> BS {
+    BS x(n);
+    char c;
+    for (int i = 0; i < n; ++i) {
+      scanf("%c", &c);
+      x[i] = c - '0';
+    }
+    scanf("%c", &c);
+    assert(c == '\n');
+    return x;
+  };
+  vc<BS> A(N);
+  FOR(i, N) A[i] = get(M);
+  BS b = get(N);
+  auto ANS = solve_linear(N, M, A, b);
+  if (ANS.empty()) {
+    printf("-1\n");
+    return;
+  }
+  int R = len(ANS) - 1;
+  printf("%d\n", R);
+  for (auto &x: ANS) {
+    string ans = x.to_string();
+    printf("%s\n", ans.c_str());
+  }
+}
+
+signed main() { solve(); }
diff --git a/linear_algebra/system_of_linear_equations_mod_2/task.md b/linear_algebra/system_of_linear_equations_mod_2/task.md
new file mode 100644
index 00000000..6e44427a
--- /dev/null
+++ b/linear_algebra/system_of_linear_equations_mod_2/task.md
@@ -0,0 +1,72 @@
+## @{keyword.statement}
+
+@{lang.en}
+
+Given $N \times M$ matrix $A$, a size $N$ vector $b$. Please calculate a (size $M$) vector $x$ s.t. $Ax = b$. We consider everything $\mathbb{F}_{2}$.
+
+For the input and output of matrices and vectors, please treat each row as a string concatenated with its components ($0$ or $1$).
+@{lang.ja}
+
+$N \times M$ 行列 $A$, 長さ $N$ のベクトル $b$ が与えられます。$Ax = b$ を満たす(長さ $M$ の)ベクトル $x$ を求めてください。ただし全ての要素は $\mathbb{F}_{2}$ で考えることとします。
+
+行列・ベクトルの入出力の際は，各行を成分（$0$ または $1$）を結合した文字列として扱ってください．
+@{lang.end}
+
+## @{keyword.constraints}
+
+- $1 \leq N \leq @{param.N_MAX}$
+- $1 \leq M \leq @{param.M_MAX}$
+- $A_{ij} \in \lbrace 0,1\rbrace$
+- $b_{i} \in \lbrace 0,1\rbrace$
+
+## @{keyword.input}
+
+```
+$N$ $M$
+$A_{0,0}A_{0,1}\cdots A_{0,M-1}$
+$A_{1,0}A_{1,1}\cdots A_{1,M-1}$
+$\vdots$
+$A_{N-1,0}A_{N-1,1}\cdots A_{N-1,M-1}$
+$b_0b_1\cdots b_{N-1}$
+```
+
+## @{keyword.output}
+
+@{lang.en}
+If there is no solution, print
+@{lang.ja}
+解が存在しない場合
+@{lang.end}
+
+```
+-1
+```
+
+@{lang.en}
+and if exists, print as follows.
+@{lang.ja}
+と出力してください．存在する場合，
+@{lang.end}
+
+
+```
+$R$
+$c_0c_1\cdots c_{M-1}$
+$d_{0,0}d_{0,1}\cdots d_{0,M-1}$
+$\vdots$
+$d_{R-1,0}d_{R-1,1}\cdots d_{R-1,M-1}$
+```
+
+@{lang.en}
+We note that $R$ is the rank of solution. $c_i$ is one of the solution. For each $j$, $d_{j,0}\cdots d_{j,M-1}$ is the basis of solution.
+@{lang.ja}
+と出力してください．ただし，$R$ は解空間の次元，$c_i$ は解のうち $1$ つとし，各 $j$ について，$d_{j,0}\cdots d_{j,M-1}$ は解空間の基底ベクトルとします．
+@{lang.end}
+
+## @{keyword.sample}
+
+@{example.example_00}
+
+@{example.example_01}
+
+@{example.example_02}
diff --git a/linear_algebra/system_of_linear_equations_mod_2/verifier.cpp b/linear_algebra/system_of_linear_equations_mod_2/verifier.cpp
new file mode 100644
index 00000000..d2afe488
--- /dev/null
+++ b/linear_algebra/system_of_linear_equations_mod_2/verifier.cpp
@@ -0,0 +1,26 @@
+#include <iostream>
+#include <cstring>
+#include "params.h"
+#include "testlib.h"
+
+using namespace std;
+
+int main() {
+  registerValidation();
+  int n = inf.readInt(1, N_MAX);
+  inf.readSpace();
+  int m = inf.readInt(1, M_MAX);
+  inf.readChar('\n');
+  for (int i = 0; i < n; i++) {
+    string S = inf.readToken();
+    inf.readChar('\n');
+    ensure(int(S.size()) == m);
+    for (auto& ch: S) { ensure(ch == '0' || ch == '1'); }
+  }
+  string S = inf.readToken();
+  inf.readChar('\n');
+  ensure(int(S.size()) == n);
+  for (auto& ch: S) { ensure(ch == '0' || ch == '1'); }
+  inf.readEof();
+  return 0;
+}