implement Bivaraite Bicycle codes as subset of 2BGA

test/test_ecc_bivaraite_bicycle_as_twobga.jl

@@ -0,0 +1,180 @@
+@testitem "ECC Bivaraite Bicycle as 2BGA" begin
+    using Hecke
+    using Hecke: group_algebra, GF, abelian_group, gens, one, FqFieldElem, GroupAlgebraElem, GroupAlgebra, FinGenAbGroup, FinGenAbGroupElem
+    using QuantumClifford.ECC: two_block_group_algebra_codes, code_k, code_n
+
+    function get_code(A::Vector{GroupAlgebraElem{FqFieldElem, GroupAlgebra{FqFieldElem, FinGenAbGroup, FinGenAbGroupElem}}}, B::Vector{GroupAlgebraElem{FqFieldElem, GroupAlgebra{FqFieldElem, FinGenAbGroup, FinGenAbGroupElem}}}, GA::GroupAlgebra{FqFieldElem, FinGenAbGroup, FinGenAbGroupElem})
+        a = sum(GA(x) for x in A)
+        b = sum(GA(x) for x in B)
+        c = two_block_group_algebra_codes(a,b)
+        return c
+    end
+
+    @testset "Reproduce Table 3 bravyi2024high" begin
+        # [[72, 12, 6]]
+        l=6; m=6
+        GA = group_algebra(GF(2), abelian_group([l, m]))
+        x, y = gens(GA)
+        A = [x^3, y, y^2]
+        B = [y^3, x, x^2]
+        c = get_code(A,B,GA)
+        @test code_n(c) == 72 &&  code_k(c) == 12
+
+        # [[90, 8, 10]]
+        l=15; m=3
+        GA = group_algebra(GF(2), abelian_group([l, m]))
+        x, y = gens(GA)
+        A = [x^9   , y   , y^2]
+        B = [one(x), x^2 , x^7]
+        c = get_code(A,B,GA)
+        @test code_n(c) == 90 &&  code_k(c) == 8
+
+        # [[108, 8, 10]]
+        l=9; m=6
+        GA = group_algebra(GF(2), abelian_group([l, m]))
+        x, y = gens(GA)
+        A = [x^3 , y , y^2]
+        B = [y^3 , x , x^2]
+        c = get_code(A,B,GA)
+        @test code_n(c) == 108 &&  code_k(c) == 8
+
+        # [[144, 12, 12]]
+        l=12; m=6
+        GA = group_algebra(GF(2), abelian_group([l, m]))
+        x, y = gens(GA)
+        A = [x^3 , y , y^2]
+        B = [y^3 , x , x^2]
+        c = get_code(A,B,GA)
+        @test code_n(c) == 144 &&  code_k(c) == 12
+
+        # [[288, 12, 12]]
+        l=12; m=12
+        GA = group_algebra(GF(2), abelian_group([l, m]))
+        x, y = gens(GA)
+        A = [x^3 , y^2, y^7]
+        B = [y^3 , x  , x^2]
+        c = get_code(A,B,GA)
+        @test code_n(c) == 288 &&  code_k(c) == 12
+
+        # [[360, 12, ≤ 24]]
+        l=30; m=6
+        GA = group_algebra(GF(2), abelian_group([l, m]))
+        x, y = gens(GA)
+        A = [x^9 , y    ,  y^2]
+        B = [y^3 , x^25 , x^26]
+        c = get_code(A,B,GA)
+        @test code_n(c) == 360 &&  code_k(c) == 12
+
+        # [[756, 16, ≤ 34]]
+        l=21; m=18
+        GA = group_algebra(GF(2), abelian_group([l, m]))
+        x, y = gens(GA)
+        A = [x^3 , y^10 , y^17]
+        B = [y^5 , x^3  , x^19]
+        c = get_code(A,B,GA)
+        @test code_n(c) == 756 &&  code_k(c) == 16
+    end
+
+    @testset "Reproduce Table 1 berthusen2024toward" begin
+        # [[72, 8, 6]]
+        l=12; m=3
+        GA = group_algebra(GF(2), abelian_group([l, m]))
+        x, y = gens(GA)
+        A = [x^9   , y ,  y^2]
+        B = [one(x), x , x^11]
+        c = get_code(A,B,GA)
+        @test code_n(c) == 72 &&  code_k(c) == 8
+
+        # [[90, 8, 6]]
+        l=9; m=5
+        GA = group_algebra(GF(2), abelian_group([l, m]))
+        x, y = gens(GA)
+        A = [x^8 , y^4 ,  y]
+        B = [y^5 , x^8 , x^7]
+        c = get_code(A,B,GA)
+        @test code_n(c) == 90 &&  code_k(c) == 8
+
+        # [[120, 8, 8]]
+        l=12; m=5
+        GA = group_algebra(GF(2), abelian_group([l, m]))
+        x, y = gens(GA)
+        A = [x^10  , y^4,   y]
+        B = [one(x), x  , x^2]
+        c = get_code(A,B,GA)
+        @test code_n(c) == 120 &&  code_k(c) == 8
+
+        # [[150, 8, 8]]
+        l=15; m=5
+        GA = group_algebra(GF(2), abelian_group([l, m]))
+        x, y = gens(GA)
+        A = [x^5 , y^2 , y^3]
+        B = [y^2 , x^7 , x^6]
+        c = get_code(A,B,GA)
+        @test code_n(c) == 150 &&  code_k(c) == 8
+
+        # [[196, 12, 8]]
+        l=14; m=7
+        GA = group_algebra(GF(2), abelian_group([l, m]))
+        x, y = gens(GA)
+        A = [x^6   , y^5 ,  y^6]
+        B = [one(x), x^4 , x^13]
+        c = get_code(A,B,GA)
+        @test code_n(c) == 196 &&  code_k(c) == 12
+    end
+
+    @testset "Reproduce Table 1 wang2024coprime" begin
+        # [[54, 8, 6]]
+        l=3; m=9
+        GA = group_algebra(GF(2), abelian_group([l, m]))
+        x, y = gens(GA)
+        A = [one(x), y^2, y^4]
+        B = [y^3   , x  , x^2]
+        c = get_code(A,B,GA)
+        @test code_n(c) == 54 &&  code_k(c) == 8
+
+        # [[98, 6, 12]]
+        l=7; m=7
+        GA = group_algebra(GF(2), abelian_group([l, m]))
+        x, y = gens(GA)
+        A = [x^3 , y^5 , y^6]
+        B = [y^2 , x^3 , x^5]
+        c = get_code(A,B,GA)
+        @test code_n(c) == 98 &&  code_k(c) == 6
+
+        # [[126, 8, 10]]
+        l=3; m=21
+        GA = group_algebra(GF(2), abelian_group([l, m]))
+        x, y = gens(GA)
+        A = [one(x), y^2, y^10]
+        B = [y^3   , x  ,  x^2]
+        c = get_code(A,B,GA)
+        @test code_n(c) == 126 &&  code_k(c) == 8
+
+        # [[150, 16, 8]]
+        l=5; m=15
+        GA = group_algebra(GF(2), abelian_group([l, m]))
+        x, y = gens(GA)
+        A = [one(x), y^6, y^8]
+        B = [y^5   , x  , x^4]
+        c = get_code(A,B,GA)
+        @test code_n(c) == 150 &&  code_k(c) == 16
+
+        # [[162, 8, 14]]
+        l=3; m=27
+        GA = group_algebra(GF(2), abelian_group([l, m]))
+        x, y = gens(GA)
+        A = [one(x), y^10, y^14]
+        B = [y^12  , x   ,  x^2]
+        c = get_code(A,B,GA)
+        @test code_n(c) == 162 &&  code_k(c) == 8
+
+        # [[180, 8, 16]]
+        l=6; m=15
+        GA = group_algebra(GF(2), abelian_group([l, m]))
+        x, y = gens(GA)
+        A = [x^3 , y   , y^2]
+        B = [y^6 , x^4 , x^5]
+        c = get_code(A,B,GA)
+        @test code_n(c) == 180 &&  code_k(c) == 8
+    end
+end