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cyclic.hpp
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#pragma once
#include <cstdint>
#include <type_traits>
/**
* Template metaprogramming struct compile-validate if the polynomial is irreducible over GF2**8
*/
template <uint8_t mod> struct is_cyclic_over_gf256 : std::false_type{
static constexpr uint8_t generators[0] = {}; ///< Generators for the given polynomial, If there is one there will be 128
};
template <> struct is_cyclic_over_gf256<0x1B> : std::true_type {
static constexpr uint8_t generators[128] = {
3, 5, 6, 9, 11, 14, 17, 18, 19, 20, 23, 24, 25, 26, 28, 30,
31, 33, 34, 35, 39, 40, 42, 44, 48, 49, 60, 62, 63, 65, 69, 70,
71, 72, 73, 75, 76, 78, 79, 82, 84, 86, 87, 88, 89, 90, 91, 95,
100, 101, 104, 105, 109, 110, 112, 113, 118, 119, 121, 122, 123, 126, 129, 132,
134, 135, 136, 138, 142, 143, 144, 147, 149, 150, 152, 153, 155, 157, 160, 164,
165, 166, 167, 169, 170, 172, 173, 178, 180, 183, 184, 185, 186, 190, 191, 192,
193, 196, 200, 201, 206, 207, 208, 214, 215, 218, 220, 221, 222, 226, 227, 229,
230, 231, 233, 234, 235, 238, 240, 241, 244, 245, 246, 248, 251, 253, 254, 255};
};
template <> struct is_cyclic_over_gf256<0x1D> : std::true_type {
static constexpr uint8_t generators[128] = {
2, 4, 6, 9, 13, 14, 16, 18, 19, 20, 22, 24, 25, 27, 29, 30,
31, 34, 35, 40, 42, 43, 48, 49, 50, 52, 57, 60, 63, 65, 66, 67,
71, 72, 73, 74, 75, 76, 81, 82, 83, 84, 88, 90, 91, 92, 93, 95,
98, 99, 104, 105, 109, 111, 112, 113, 118, 119, 121, 122, 123, 126, 128, 129,
131, 133, 135, 136, 137, 140, 141, 142, 144, 148, 149, 151, 154, 155, 157, 158,
159, 162, 163, 164, 165, 170, 171, 175, 176, 177, 178, 183, 187, 188, 189, 192,
194, 198, 199, 200, 201, 202, 203, 204, 209, 210, 211, 212, 213, 216, 218, 222,
224, 225, 227, 229, 232, 234, 236, 238, 240, 243, 246, 247, 248, 249, 250, 254};
};
template <> struct is_cyclic_over_gf256<0x2B> : std::true_type {
static constexpr uint8_t generators[128] = {
2, 4, 6, 7, 9, 10, 13, 16, 20, 21, 22, 23, 34, 38, 43, 44,
45, 48, 49, 54, 55, 56, 57, 58, 59, 62, 63, 65, 67, 68, 70, 71,
73, 74, 75, 76, 77, 78, 81, 83, 87, 89, 90, 92, 94, 96, 97, 98,
100, 102, 104, 112, 113, 115, 116, 117, 118, 119, 124, 125, 128, 129, 132, 133,
134, 135, 137, 139, 140, 143, 144, 146, 147, 148, 149, 153, 155, 157, 159, 160,
162, 163, 164, 167, 168, 170, 176, 178, 181, 182, 183, 184, 186, 190, 191, 193,
194, 195, 198, 199, 200, 202, 203, 204, 206, 210, 211, 212, 213, 216, 222, 223,
227, 228, 229, 231, 233, 238, 240, 241, 242, 243, 244, 245, 246, 251, 252, 253};
};
template <> struct is_cyclic_over_gf256<0x2D> : std::true_type {
static constexpr uint8_t generators[128] = {
2, 4, 6, 7, 9, 10, 11, 12, 13, 16, 20, 21, 22, 23, 26, 27,
29, 30, 34, 39, 42, 45, 46, 48, 55, 56, 57, 60, 61, 63, 65, 67,
68, 69, 70, 71, 72, 74, 75, 76, 78, 79, 80, 81, 82, 91, 93, 94,
97, 100, 102, 104, 105, 114, 115, 117, 118, 119, 121, 124, 126, 127, 128, 129,
130, 131, 134, 139, 140, 143, 145, 146, 148, 149, 150, 151, 153, 154, 155, 158,
159, 161, 163, 166, 167, 168, 170, 171, 172, 173, 174, 176, 184, 185, 187, 188,
195, 196, 197, 199, 200, 201, 202, 204, 206, 207, 208, 209, 210, 211, 212, 213,
216, 217, 218, 222, 223, 224, 226, 229, 232, 233, 235, 237, 240, 243, 246, 253};
};
template <> struct is_cyclic_over_gf256<0x39> : std::true_type {
static constexpr uint8_t generators[128] = {
3, 5, 6, 7, 10, 11, 12, 13, 14, 17, 20, 21, 22, 23, 24, 26,
28, 29, 34, 37, 40, 41, 42, 44, 45, 48, 52, 56, 58, 63, 68, 69,
71, 73, 77, 79, 80, 81, 82, 83, 84, 87, 88, 89, 90, 92, 93, 95,
96, 99, 103, 104, 105, 112, 113, 115, 116, 117, 121, 125, 126, 127, 131, 136,
138, 142, 146, 148, 150, 151, 153, 154, 157, 160, 162, 163, 164, 165, 166, 168,
173, 174, 175, 178, 179, 180, 181, 183, 184, 185, 186, 187, 190, 191, 192, 193,
195, 197, 198, 199, 202, 203, 205, 206, 208, 210, 211, 215, 221, 224, 226, 227,
230, 231, 232, 233, 234, 235, 237, 239, 242, 245, 247, 249, 252, 253, 254, 255};
};
template <> struct is_cyclic_over_gf256<0x3F> : std::true_type {
static constexpr uint8_t generators[128] = {
3, 5, 6, 7, 11, 12, 14, 17, 20, 21, 22, 23, 34, 35, 36, 37,
42, 43, 44, 45, 46, 47, 48, 53, 56, 57, 62, 67, 69, 70, 72, 74,
77, 78, 80, 82, 83, 84, 87, 88, 89, 91, 92, 94, 95, 96, 99, 101,
102, 103, 105, 112, 113, 114, 115, 117, 118, 119, 124, 125, 130, 131, 133, 136,
137, 138, 139, 140, 141, 142, 144, 151, 155, 156, 157, 158, 160, 163, 165, 166,
167, 168, 169, 171, 172, 173, 178, 179, 180, 184, 185, 190, 191, 192, 195, 201,
203, 204, 206, 207, 209, 210, 212, 213, 217, 218, 219, 221, 222, 224, 227, 229,
230, 234, 235, 236, 237, 238, 241, 242, 245, 247, 248, 249, 250, 251, 254, 255};
};
template <> struct is_cyclic_over_gf256<0x4D> : std::true_type {
static constexpr uint8_t generators[128] = {
2, 3, 4, 5, 7, 9, 10, 13, 16, 17, 18, 19, 21, 22, 24, 26,
31, 39, 40, 41, 42, 43, 44, 45, 46, 47, 56, 57, 60, 61, 62, 65,
66, 68, 72, 73, 75, 76, 77, 78, 79, 81, 82, 83, 86, 89, 92, 94,
96, 99, 100, 101, 102, 103, 106, 108, 110, 111, 116, 117, 118, 127, 128, 132,
133, 134, 135, 137, 140, 141, 142, 147, 148, 150, 151, 158, 163, 165, 166, 167,
168, 170, 171, 173, 174, 175, 176, 180, 183, 185, 186, 187, 190, 192, 193, 194,
196, 197, 200, 203, 207, 208, 210, 213, 215, 218, 222, 224, 225, 226, 227, 229,
232, 233, 234, 235, 236, 238, 239, 240, 242, 243, 246, 248, 249, 252, 253, 255};
};
template <> struct is_cyclic_over_gf256<0x5F> : std::true_type {
static constexpr uint8_t generators[128] = {
2, 3, 4, 5, 7, 11, 12, 14, 16, 17, 18, 19, 21, 23, 25, 29,
30, 40, 41, 43, 44, 45, 52, 56, 57, 58, 59, 60, 61, 62, 63, 66,
69, 70, 71, 74, 77, 78, 80, 84, 86, 88, 90, 91, 92, 93, 94, 95,
96, 97, 98, 99, 100, 102, 106, 108, 110, 111, 113, 114, 115, 127, 128, 130,
131, 134, 135, 136, 138, 139, 142, 144, 145, 147, 148, 149, 150, 151, 152, 153,
154, 155, 157, 162, 165, 167, 169, 170, 171, 174, 175, 178, 183, 184, 187, 188,
191, 192, 193, 195, 196, 197, 199, 200, 202, 203, 206, 208, 209, 211, 212, 216,
218, 221, 231, 232, 233, 235, 236, 241, 244, 245, 246, 248, 249, 250, 251, 255};
};
template <> struct is_cyclic_over_gf256<0x63> : std::true_type {
static constexpr uint8_t generators[128] = {
2, 3, 4, 5, 12, 13, 14, 16, 17, 22, 26, 27, 29, 30, 31, 36,
38, 39, 40, 41, 42, 43, 44, 47, 50, 54, 55, 57, 59, 60, 63, 66,
70, 71, 72, 74, 75, 77, 78, 80, 81, 83, 84, 89, 91, 92, 93, 95,
96, 97, 98, 99, 100, 106, 109, 112, 119, 121, 122, 123, 125, 127, 128, 130,
131, 134, 136, 146, 147, 149, 152, 153, 155, 158, 164, 167, 169, 170, 171, 172,
174, 175, 176, 177, 178, 180, 181, 185, 186, 189, 191, 192, 194, 196, 201, 202,
205, 206, 207, 208, 209, 210, 211, 212, 217, 219, 220, 222, 223, 224, 225, 228,
229, 230, 232, 233, 236, 242, 243, 244, 245, 246, 247, 248, 249, 250, 251, 255};
};
template <> struct is_cyclic_over_gf256<0x65> : std::true_type {
static constexpr uint8_t generators[128] = {
2, 3, 4, 5, 9, 10, 11, 16, 17, 23, 24, 25, 26, 28, 29, 33,
36, 37, 40, 42, 44, 47, 52, 53, 54, 57, 59, 60, 61, 62, 63, 65,
68, 69, 70, 73, 74, 76, 78, 79, 82, 83, 86, 88, 89, 90, 92, 94,
99, 100, 101, 102, 103, 106, 109, 112, 119, 121, 122, 123, 124, 127, 128, 132,
133, 134, 135, 138, 139, 140, 141, 142, 143, 147, 150, 151, 152, 153, 156, 157,
159, 161, 162, 163, 164, 166, 169, 170, 175, 177, 178, 179, 181, 182, 184, 185,
186, 187, 190, 192, 193, 194, 196, 197, 198, 201, 203, 209, 211, 213, 214, 216,
217, 220, 221, 222, 224, 225, 227, 231, 234, 236, 237, 240, 249, 252, 253, 255};
};
template <> struct is_cyclic_over_gf256<0x69> : std::true_type {
static constexpr uint8_t generators[128] = {
2, 3, 4, 5, 16, 17, 24, 27, 28, 30, 33, 35, 37, 39, 41, 42,
43, 44, 46, 47, 49, 50, 52, 55, 57, 58, 59, 61, 62, 63, 67, 72,
75, 76, 77, 78, 79, 87, 88, 90, 92, 93, 94, 95, 97, 103, 104, 105,
112, 113, 114, 115, 116, 117, 118, 119, 128, 129, 131, 132, 133, 134, 135, 136,
137, 138, 140, 144, 145, 146, 148, 151, 152, 153, 157, 160, 162, 165, 166, 170,
172, 173, 174, 175, 177, 178, 179, 180, 182, 183, 189, 190, 192, 196, 197, 198,
199, 200, 202, 204, 207, 212, 214, 216, 218, 219, 220, 222, 223, 224, 225, 229,
233, 235, 237, 238, 239, 240, 241, 243, 245, 248, 249, 250, 251, 253, 254, 255};
};
template <> struct is_cyclic_over_gf256<0x71> : std::true_type {
static constexpr uint8_t generators[128] = {
2, 4, 6, 7, 10, 11, 12, 16, 20, 21, 23, 27, 28, 30, 31, 33,
35, 36, 37, 38, 39, 41, 45, 47, 52, 56, 57, 58, 61, 63, 68, 69,
71, 72, 73, 75, 78, 79, 80, 88, 89, 91, 92, 96, 97, 98, 99, 100,
104, 105, 106, 108, 109, 111, 113, 115, 118, 119, 124, 125, 128, 130, 131, 132,
133, 134, 135, 137, 139, 141, 143, 145, 147, 149, 153, 154, 155, 157, 160, 161,
162, 163, 164, 165, 168, 170, 172, 174, 175, 176, 180, 184, 186, 187, 190, 191,
194, 195, 199, 200, 201, 202, 204, 205, 206, 207, 210, 211, 212, 214, 216, 220,
221, 223, 224, 228, 230, 231, 232, 234, 235, 236, 237, 243, 244, 247, 248, 251};
};
template <> struct is_cyclic_over_gf256<0x77> : std::true_type {
static constexpr uint8_t generators[128] = {
3, 5, 6, 7, 10, 12, 13, 17, 20, 21, 22, 24, 25, 27, 28, 39,
41, 42, 44, 45, 46, 49, 50, 52, 53, 54, 55, 56, 59, 61, 68, 73,
74, 75, 78, 80, 81, 82, 88, 90, 91, 92, 93, 99, 100, 101, 102, 103,
104, 105, 106, 108, 109, 110, 112, 113, 117, 118, 124, 125, 133, 135, 138, 141,
143, 146, 147, 148, 149, 150, 153, 156, 158, 159, 160, 161, 162, 163, 164, 165,
166, 168, 169, 173, 176, 177, 179, 180, 184, 185, 189, 190, 192, 195, 196, 197,
198, 200, 201, 204, 205, 206, 207, 208, 209, 210, 212, 213, 216, 221, 224, 226,
227, 229, 234, 236, 239, 241, 242, 244, 247, 248, 249, 250, 251, 252, 253, 255};
};
template <> struct is_cyclic_over_gf256<0x7B> : std::true_type {
static constexpr uint8_t generators[128] = {
9, 11, 13, 14, 22, 23, 26, 27, 28, 29, 33, 35, 36, 37, 38, 42,
43, 45, 49, 50, 53, 54, 55, 56, 62, 63, 65, 66, 67, 69, 73, 74,
75, 76, 78, 81, 84, 86, 87, 88, 89, 91, 92, 95, 99, 100, 104, 105,
110, 111, 114, 115, 116, 117, 124, 125, 129, 131, 132, 134, 135, 138, 139, 140,
143, 144, 145, 146, 148, 150, 153, 156, 157, 161, 162, 165, 166, 167, 171, 172,
174, 175, 176, 177, 178, 179, 180, 182, 183, 184, 185, 187, 193, 196, 197, 198,
200, 202, 203, 205, 207, 208, 210, 211, 216, 218, 219, 220, 221, 222, 223, 224,
228, 229, 232, 235, 237, 238, 239, 242, 243, 245, 247, 248, 249, 250, 253, 254};
};
template <> struct is_cyclic_over_gf256<0x87> : std::true_type {
static constexpr uint8_t generators[128] = {
2, 4, 7, 10, 11, 12, 14, 16, 18, 21, 26, 27, 29, 30, 34, 35,
37, 38, 39, 41, 45, 46, 48, 52, 55, 56, 60, 61, 62, 63, 66, 67,
68, 69, 70, 71, 72, 73, 74, 80, 82, 84, 88, 89, 90, 92, 93, 94,
96, 97, 100, 101, 102, 103, 106, 111, 115, 118, 119, 121, 122, 123, 125, 127,
128, 129, 131, 132, 135, 138, 139, 142, 144, 145, 150, 153, 154, 156, 157, 158,
160, 161, 162, 163, 166, 169, 172, 173, 174, 181, 183, 185, 187, 188, 190, 191,
193, 194, 195, 196, 200, 201, 202, 204, 205, 211, 212, 214, 216, 217, 218, 219,
227, 228, 229, 230, 231, 233, 234, 235, 238, 239, 240, 246, 247, 251, 252, 253};
};
template <> struct is_cyclic_over_gf256<0x8B> : std::true_type {
static constexpr uint8_t generators[128] = {
6, 10, 11, 12, 18, 19, 20, 22, 23, 24, 25, 29, 33, 34, 36, 38,
40, 44, 46, 47, 48, 49, 50, 54, 55, 57, 58, 59, 62, 66, 67, 68,
69, 72, 73, 74, 79, 80, 83, 87, 91, 92, 93, 95, 98, 100, 101, 102,
103, 108, 109, 110, 113, 114, 115, 116, 117, 121, 123, 125, 126, 127, 129, 130,
131, 133, 135, 136, 137, 141, 142, 143, 144, 145, 148, 149, 151, 152, 155, 158,
159, 161, 163, 165, 166, 174, 175, 176, 181, 184, 185, 186, 187, 188, 190, 196,
199, 200, 202, 203, 204, 205, 210, 213, 215, 216, 218, 220, 221, 225, 228, 229,
230, 231, 234, 235, 236, 238, 241, 242, 243, 246, 248, 249, 250, 252, 253, 254};
};
template <> struct is_cyclic_over_gf256<0x8D> : std::true_type {
static constexpr uint8_t generators[128] = {
2, 3, 4, 5, 7, 9, 12, 16, 17, 18, 19, 21, 24, 26, 28, 30,
33, 38, 40, 42, 44, 45, 50, 54, 56, 57, 58, 60, 61, 65, 67, 72,
80, 82, 87, 88, 89, 91, 92, 93, 96, 97, 98, 99, 100, 101, 102, 105,
106, 108, 109, 110, 111, 118, 124, 125, 126, 127, 128, 129, 131, 132, 133, 136,
137, 138, 140, 141, 142, 143, 144, 145, 146, 148, 149, 150, 156, 159, 162, 168,
169, 171, 172, 177, 180, 183, 184, 185, 187, 188, 189, 193, 197, 198, 199, 201,
203, 205, 209, 211, 212, 213, 214, 215, 217, 221, 224, 225, 227, 229, 231, 232,
233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 245, 249, 251, 252, 255};
};
template <> struct is_cyclic_over_gf256<0x9F> : std::true_type {
static constexpr uint8_t generators[128] = {
3, 5, 6, 11, 17, 18, 20, 23, 24, 25, 26, 27, 30, 31, 36, 38,
39, 40, 44, 45, 46, 47, 48, 49, 52, 53, 54, 55, 57, 58, 60, 63,
66, 67, 69, 73, 76, 77, 78, 79, 82, 83, 86, 87, 88, 91, 97, 98,
99, 100, 103, 106, 109, 110, 116, 117, 121, 122, 123, 124, 130, 135, 136, 137,
138, 140, 141, 143, 144, 146, 147, 149, 150, 155, 157, 158, 160, 162, 164, 165,
170, 171, 172, 175, 177, 179, 180, 181, 184, 185, 186, 188, 189, 191, 192, 193,
195, 198, 200, 201, 202, 203, 205, 208, 209, 211, 218, 219, 222, 223, 226, 228,
229, 230, 231, 233, 234, 238, 239, 240, 243, 244, 246, 247, 248, 252, 253, 255};
};
template <> struct is_cyclic_over_gf256<0xA3> : std::true_type {
static constexpr uint8_t generators[128] = {
3, 5, 6, 9, 10, 12, 13, 17, 18, 19, 20, 23, 24, 25, 26, 27,
29, 31, 33, 35, 38, 39, 46, 50, 52, 55, 58, 59, 61, 62, 65, 66,
68, 70, 71, 72, 73, 75, 79, 80, 81, 82, 92, 93, 96, 97, 100, 101,
102, 103, 104, 108, 110, 111, 113, 117, 118, 119, 122, 123, 124, 125, 126, 127,
129, 130, 131, 132, 133, 135, 136, 137, 142, 143, 144, 145, 149, 152, 153, 155,
156, 157, 158, 160, 162, 164, 165, 166, 167, 169, 174, 179, 182, 189, 190, 191,
192, 193, 194, 197, 204, 206, 211, 213, 216, 217, 218, 220, 223, 226, 227, 230,
231, 232, 235, 237, 238, 239, 242, 244, 245, 246, 248, 249, 250, 252, 254, 255};
};
template <> struct is_cyclic_over_gf256<0xA9> : std::true_type {
static constexpr uint8_t generators[128] = {
2, 3, 4, 5, 6, 7, 9, 14, 16, 17, 19, 20, 21, 22, 23, 24,
25, 29, 31, 33, 34, 35, 36, 37, 40, 45, 50, 52, 55, 56, 57, 59,
60, 61, 62, 65, 71, 72, 73, 76, 77, 78, 79, 84, 87, 88, 89, 90,
91, 93, 94, 101, 105, 106, 108, 112, 113, 117, 118, 127, 128, 129, 130, 131,
132, 133, 135, 137, 141, 147, 148, 149, 150, 152, 155, 156, 157, 160, 161, 162,
164, 165, 166, 167, 168, 169, 170, 172, 176, 177, 179, 181, 182, 183, 184, 185,
187, 188, 189, 190, 191, 192, 200, 203, 204, 205, 206, 211, 212, 217, 218, 225,
227, 228, 229, 230, 232, 233, 234, 239, 240, 241, 242, 245, 248, 252, 254, 255};
};
template <> struct is_cyclic_over_gf256<0xB1> : std::true_type {
static constexpr uint8_t generators[128] = {
6, 7, 9, 10, 11, 12, 13, 19, 20, 21, 25, 26, 28, 29, 30, 34,
36, 37, 42, 44, 45, 47, 48, 49, 53, 55, 56, 57, 59, 60, 65, 66,
68, 69, 70, 71, 72, 73, 75, 76, 77, 79, 80, 81, 83, 88, 93, 96,
98, 104, 105, 109, 111, 113, 114, 116, 117, 119, 121, 124, 125, 126, 130, 132,
133, 135, 138, 139, 140, 143, 145, 146, 147, 148, 152, 153, 155, 158, 159, 160,
161, 166, 167, 170, 171, 173, 174, 179, 180, 183, 187, 188, 194, 195, 197, 200,
201, 202, 206, 207, 208, 209, 212, 214, 215, 217, 218, 219, 220, 221, 223, 224,
225, 227, 229, 230, 231, 232, 234, 235, 236, 237, 239, 240, 245, 246, 251, 254};
};
template <> struct is_cyclic_over_gf256<0xBD> : std::true_type {
static constexpr uint8_t generators[128] = {
7, 9, 14, 18, 19, 21, 22, 25, 26, 27, 28, 31, 33, 35, 36, 41,
42, 43, 44, 45, 46, 49, 50, 52, 53, 54, 56, 58, 59, 63, 65, 70,
72, 73, 76, 77, 78, 79, 84, 86, 87, 88, 90, 91, 92, 95, 97, 98,
99, 100, 101, 103, 104, 108, 109, 114, 118, 119, 123, 124, 125, 126, 130, 131,
132, 133, 135, 138, 140, 141, 143, 145, 152, 153, 154, 156, 157, 158, 159, 162,
163, 165, 166, 167, 169, 172, 174, 175, 179, 180, 181, 182, 183, 184, 185, 191,
193, 194, 195, 202, 203, 205, 206, 208, 209, 210, 212, 213, 215, 216, 219, 224,
225, 228, 232, 234, 237, 238, 239, 241, 245, 246, 248, 249, 250, 251, 252, 254};
};
template <> struct is_cyclic_over_gf256<0xC3> : std::true_type {
static constexpr uint8_t generators[128] = {
2, 3, 4, 5, 6, 7, 9, 14, 16, 17, 19, 20, 21, 22, 23, 25,
26, 30, 31, 33, 37, 39, 40, 41, 43, 44, 45, 47, 48, 49, 50, 54,
55, 56, 60, 65, 67, 72, 73, 74, 75, 77, 79, 82, 84, 90, 91, 92,
93, 94, 95, 98, 104, 106, 108, 113, 115, 118, 119, 127, 128, 129, 130, 135,
136, 137, 139, 140, 145, 149, 150, 151, 152, 155, 156, 157, 159, 160, 161, 163,
165, 167, 170, 181, 183, 185, 190, 192, 194, 195, 198, 200, 201, 202, 203, 204,
205, 207, 208, 210, 211, 212, 213, 214, 215, 217, 218, 219, 220, 221, 223, 225,
227, 228, 229, 232, 234, 235, 236, 241, 244, 248, 250, 251, 252, 253, 254, 255};
};
template <> struct is_cyclic_over_gf256<0xCF> : std::true_type {
static constexpr uint8_t generators[128] = {
2, 4, 6, 10, 11, 12, 14, 16, 18, 19, 20, 22, 25, 26, 28, 29,
30, 31, 33, 37, 39, 41, 43, 46, 47, 49, 50, 52, 53, 58, 68, 69,
71, 78, 79, 80, 82, 83, 84, 86, 88, 90, 91, 93, 96, 97, 98, 99,
102, 103, 105, 108, 110, 111, 112, 113, 115, 118, 122, 123, 124, 125, 126, 127,
128, 129, 130, 132, 134, 135, 139, 140, 141, 142, 144, 145, 146, 148, 150, 154,
155, 158, 159, 160, 163, 169, 170, 171, 174, 177, 179, 180, 181, 183, 185, 191,
194, 197, 200, 201, 202, 203, 204, 207, 212, 213, 214, 219, 223, 224, 225, 227,
228, 229, 231, 234, 238, 239, 240, 241, 246, 247, 248, 250, 251, 252, 253, 254};
};
template <> struct is_cyclic_over_gf256<0xD7> : std::true_type {
static constexpr uint8_t generators[128] = {
7, 9, 14, 18, 19, 21, 23, 25, 27, 28, 29, 31, 33, 35, 36, 38,
39, 42, 45, 46, 47, 49, 50, 54, 56, 57, 58, 61, 62, 63, 65, 66,
67, 72, 73, 75, 76, 78, 83, 84, 90, 91, 92, 93, 94, 95, 97, 98,
99, 100, 101, 103, 105, 108, 109, 112, 113, 116, 122, 124, 125, 126, 129, 130,
132, 133, 134, 135, 137, 140, 142, 144, 145, 146, 149, 150, 152, 153, 156, 161,
163, 166, 167, 168, 169, 171, 180, 182, 184, 186, 187, 188, 190, 191, 194, 196,
197, 198, 200, 202, 203, 206, 207, 210, 211, 213, 216, 217, 218, 219, 223, 224,
225, 226, 228, 229, 230, 231, 239, 243, 244, 245, 247, 248, 250, 251, 252, 253};
};
template <> struct is_cyclic_over_gf256<0xDD> : std::true_type {
static constexpr uint8_t generators[128] = {
6, 7, 10, 11, 12, 13, 14, 19, 20, 21, 24, 26, 27, 29, 31, 34,
35, 37, 38, 40, 44, 45, 47, 48, 54, 55, 56, 57, 59, 63, 68, 69,
70, 75, 79, 80, 81, 82, 83, 84, 86, 88, 90, 91, 93, 94, 95, 101,
102, 104, 105, 109, 110, 112, 114, 115, 116, 118, 121, 124, 125, 126, 129, 133,
136, 140, 142, 145, 146, 147, 148, 149, 150, 152, 153, 155, 157, 158, 159, 162,
163, 164, 165, 166, 168, 169, 174, 176, 177, 179, 181, 182, 183, 186, 187, 188,
189, 190, 192, 193, 197, 199, 202, 203, 204, 205, 208, 215, 216, 218, 223, 224,
225, 227, 230, 231, 235, 236, 237, 239, 242, 243, 245, 247, 248, 250, 251, 252};
};
template <> struct is_cyclic_over_gf256<0xE7> : std::true_type {
static constexpr uint8_t generators[128] = {
2, 4, 6, 13, 16, 18, 20, 22, 24, 25, 28, 29, 30, 31, 34, 35,
36, 37, 38, 39, 40, 42, 44, 46, 52, 53, 54, 56, 57, 58, 59, 60,
66, 67, 70, 71, 73, 75, 81, 86, 87, 91, 92, 93, 94, 95, 97, 99,
100, 101, 103, 106, 109, 111, 114, 115, 121, 122, 123, 125, 128, 130, 131, 135,
136, 138, 141, 142, 143, 144, 145, 149, 151, 154, 156, 157, 158, 159, 161, 164,
165, 166, 167, 168, 170, 171, 172, 178, 179, 182, 183, 185, 186, 187, 192, 193,
196, 198, 200, 201, 204, 207, 209, 210, 211, 213, 214, 215, 216, 217, 220, 223,
227, 229, 231, 232, 234, 236, 237, 238, 240, 241, 243, 244, 245, 247, 248, 252};
};
template <> struct is_cyclic_over_gf256<0xF3> : std::true_type {
static constexpr uint8_t generators[128] = {
6, 10, 12, 13, 18, 19, 20, 22, 23, 26, 30, 31, 33, 34, 35, 36,
37, 43, 44, 46, 47, 48, 50, 53, 54, 57, 58, 59, 60, 67, 68, 70,
73, 76, 78, 79, 80, 81, 86, 87, 89, 90, 91, 93, 96, 97, 98, 99,
101, 108, 109, 111, 114, 115, 116, 117, 118, 121, 122, 124, 126, 127, 129, 130,
131, 132, 134, 135, 137, 138, 139, 142, 144, 147, 148, 149, 152, 156, 157, 158,
159, 160, 161, 165, 166, 167, 173, 175, 176, 177, 180, 183, 184, 188, 191, 196,
197, 200, 202, 205, 206, 208, 209, 210, 211, 212, 215, 217, 221, 225, 227, 230,
231, 233, 234, 235, 238, 239, 240, 241, 244, 246, 247, 248, 251, 252, 253, 254};
};
template <> struct is_cyclic_over_gf256<0xF5> : std::true_type {
static constexpr uint8_t generators[128] = {
2, 3, 4, 5, 7, 10, 14, 16, 17, 18, 19, 21, 24, 27, 29, 30,
33, 36, 40, 41, 44, 45, 46, 50, 53, 56, 57, 60, 63, 67, 68, 71,
73, 74, 75, 78, 79, 84, 87, 90, 96, 98, 99, 100, 101, 102, 103, 104,
106, 108, 109, 110, 111, 113, 124, 125, 126, 127, 128, 130, 133, 134, 136, 137,
138, 139, 140, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 155, 157, 158,
161, 164, 167, 171, 172, 173, 174, 176, 181, 185, 186, 188, 189, 190, 191, 193,
194, 195, 198, 207, 208, 210, 211, 214, 215, 216, 218, 220, 228, 230, 232, 234,
235, 237, 238, 239, 240, 241, 243, 244, 245, 246, 247, 250, 251, 253, 254, 255};
};
template <> struct is_cyclic_over_gf256<0xF9> : std::true_type {
static constexpr uint8_t generators[128] = {
3, 5, 7, 9, 10, 12, 13, 17, 18, 21, 24, 26, 28, 29, 34, 37,
39, 40, 41, 42, 43, 45, 48, 49, 52, 53, 55, 56, 58, 61, 65, 68,
71, 72, 74, 75, 77, 78, 79, 80, 81, 82, 83, 86, 87, 89, 90, 91,
96, 97, 98, 99, 102, 103, 106, 110, 112, 113, 117, 121, 122, 123, 124, 127,
130, 131, 133, 136, 142, 143, 144, 145, 148, 149, 151, 155, 156, 157, 158, 159,
160, 161, 164, 165, 166, 168, 169, 171, 175, 180, 181, 182, 183, 185, 189, 190,
194, 197, 198, 199, 202, 204, 205, 206, 207, 208, 211, 212, 213, 215, 217, 218,
224, 226, 228, 229, 231, 232, 238, 239, 242, 243, 246, 248, 250, 253, 254, 255};
};