diff --git a/test/Project.toml b/test/Project.toml
index cd15ae310..c69088264 100644
--- a/test/Project.toml
+++ b/test/Project.toml
@@ -16,6 +16,7 @@ LDPCDecoders = "3c486d74-64b9-4c60-8b1a-13a564e77efb"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 MacroTools = "1914dd2f-81c6-5fcd-8719-6d5c9610ff09"
 Nemo = "2edaba10-b0f1-5616-af89-8c11ac63239a"
+Oscar = "f1435218-dba5-11e9-1e4d-f1a5fab5fc13"
 PyQDecoders = "17f5de1a-9b79-4409-a58d-4d45812840f7"
 Quantikz = "b0d11df0-eea3-4d79-b4a5-421488cbf74b"
 QuantumInterface = "5717a53b-5d69-4fa3-b976-0bf2f97ca1e5"
diff --git a/test/test_ecc_dihedral2bga.jl b/test/test_ecc_dihedral2bga.jl
new file mode 100644
index 000000000..dd6276f45
--- /dev/null
+++ b/test/test_ecc_dihedral2bga.jl
@@ -0,0 +1,294 @@
+@testitem "ECC 2BGA Reprroduce Table 3 lin2024quantum" begin
+    using Nemo: FqFieldElem
+    using Hecke: group_algebra, GF, abelian_group, gens, quo, one, GroupAlgebra
+    using QuantumClifford.ECC
+    using QuantumClifford.ECC: code_k, code_n, two_block_group_algebra_codes
+    using Oscar: free_group, small_group_identification, describe, order, FPGroupElem, FPGroup, FPGroupElem
+
+    function get_code(a_elts::Vector{FPGroupElem}, b_elts::Vector{FPGroupElem}, F2G::GroupAlgebra{FqFieldElem, FPGroup, FPGroupElem})
+        a = sum(F2G(x) for x in a_elts)
+        b = sum(F2G(x) for x in b_elts)
+        c = two_block_group_algebra_codes(a,b)
+        return c
+    end
+
+    @testset "Reproduce Table 3 of lin2024quantum" begin
+        # [[24, 8, 3]]
+        m = 6
+        F = free_group(["r", "s"])
+        r, s = gens(F)
+        G, = quo(F, [r^m, s^2, (r*s)^2])
+        F2G = group_algebra(GF(2), G)
+        r, s = gens(G)
+        a_elts = [one(G), r^4]
+        b_elts = [one(G), s*r^4, r^3, r^4, s*r^2, r]
+        c = get_code(a_elts, b_elts, F2G)
+        @test order(G) == 2*m
+        @test describe(G) == "D$(m*2)"
+        @test code_n(c) == 24 && code_k(c) == 8
+        # Oscar.describe(Oscar.small_group(2*m, 4)) is D₁₂, cross-check it with G
+        @test small_group_identification(G) == (order(G), 4)
+
+        # [[24, 12, 2]]
+        F = free_group(["r", "s"])
+        r, s = gens(F)
+        G, = quo(F, [r^m, s^2, (r*s)^2])
+        F2G = group_algebra(GF(2), G)
+        r, s = gens(G)
+        a_elts = [one(G), r^3]
+        b_elts = [one(G), s*r, r^3, r^4, s*r^4, r]
+        c = get_code(a_elts, b_elts, F2G)
+        @test order(G) == 2*m
+        @test describe(G) == "D$(m*2)"
+        @test code_n(c) == 24 && code_k(c) == 12
+        # Oscar.describe(Oscar.small_group(2*m, 4)) is D₁₂, cross-check it with G
+        @test small_group_identification(G) == (order(G), 4)
+
+        # [[32, 8, 4]]
+        m = 8
+        F = free_group(["r", "s"])
+        r, s = gens(F)
+        G, = quo(F, [r^m, s^2, (r*s)^2])
+        F2G = group_algebra(GF(2), G)
+        r, s = gens(G)
+        a_elts = [one(G), r^2]
+        b_elts = [one(G), s*r^5, s*r^4, r^2, s*r^7, s*r^6]
+        c = get_code(a_elts, b_elts, F2G)
+        @test order(G) == 2*m
+        @test describe(G) == "D$(m*2)"
+        @test code_n(c) == 32 && code_k(c) == 8
+        # Oscar.describe(Oscar.small_group(2*m, 7)) is D₁₆, cross-check it with G
+        @test small_group_identification(G) == (order(G), 7)
+
+        # [[32, 16, 2]]
+        F = free_group(["r", "s"])
+        r, s = gens(F)
+        G, = quo(F, [r^m, s^2, (r*s)^2])
+        F2G = group_algebra(GF(2), G)
+        r, s = gens(G)
+        a_elts = [one(G), r^4]
+        b_elts = [one(G), s*r^3, s*r^6, r^4, s*r^7, s*r^2]
+        c = get_code(a_elts, b_elts, F2G)
+        @test order(G) == 2*m
+        @test describe(G) == "D$(m*2)"
+        @test code_n(c) == 32 && code_k(c) == 16
+        # Oscar.describe(Oscar.small_group(2*m, 7)) is D₁₆, cross-check it with G
+        @test small_group_identification(G) == (order(G), 7)
+
+        # [[36, 12, 3]]
+        m = 9
+        F = free_group(["r", "s"])
+        r, s = gens(F)
+        G, = quo(F, [r^m, s^2, (r*s)^2])
+        F2G = group_algebra(GF(2), G)
+        r, s = gens(G)
+        a_elts = [one(G), r^3]
+        b_elts = [one(G), s, r, r^3, s*r^3, r^4]
+        c = get_code(a_elts, b_elts, F2G)
+        @test order(G) == 2*m
+        @test describe(G) == "D$(m*2)"
+        @test code_n(c) == 36 && code_k(c) == 12
+        # Oscar.describe(Oscar.small_group(2*m, 1)) is D₁₈, cross-check it with G
+        @test small_group_identification(G) == (order(G), 1)
+
+        # [[40, 8, 5]]
+        m = 10
+        F = free_group(["r", "s"])
+        r, s = gens(F)
+        G, = quo(F, [r^m, s^2, (r*s)^2])
+        F2G = group_algebra(GF(2), G)
+        r, s = gens(G)
+        a_elts = [one(G), r^2]
+        b_elts = [one(G), s*r^4, r^5, r^2, s*r^6, r]
+        c = get_code(a_elts, b_elts, F2G)
+        @test order(G) == 2*m
+        @test describe(G) == "D$(m*2)"
+        @test code_n(c) == 40 && code_k(c) == 8
+        # Oscar.describe(Oscar.small_group(2*m, 4)) is D₂₀, cross-check it with G
+        @test small_group_identification(G) == (order(G), 4)
+
+        # [[40, 20, 2]]
+        F = free_group(["r", "s"])
+        r, s = gens(F)
+        G, = quo(F, [r^m, s^2, (r*s)^2])
+        F2G = group_algebra(GF(2), G)
+        r, s = gens(G)
+        a_elts = [one(G), r^5]
+        b_elts = [one(G), s*r^2, r^5, r^6, s*r^7, r]
+        c = get_code(a_elts, b_elts, F2G)
+        @test order(G) == 2*m
+        @test describe(G) == "D$(m*2)"
+        @test code_n(c) == 40 && code_k(c) == 20
+        # Oscar.describe(Oscar.small_group(2*m, 4)) is D₂₀, cross-check it with G
+        @test small_group_identification(G) == (order(G), 4)
+
+        # [[48, 8, 6]]
+        m = 12
+        F = free_group(["r", "s"])
+        r, s = gens(F)
+        G, = quo(F, [r^m, s^2, (r*s)^2])
+        F2G = group_algebra(GF(2), G)
+        r, s = gens(G)
+        a_elts = [one(G), r^10]
+        b_elts = [one(G), s*r^8, r^9, r^4, s*r^2, r^5]
+        c = get_code(a_elts, b_elts, F2G)
+        @test order(G) == 2*m
+        @test describe(G) == "D$(m*2)"
+        @test code_n(c) == 48 && code_k(c) == 8
+        # Oscar.describe(Oscar.small_group(2*m, 6)) is D₂₄, cross-check it with G
+        @test small_group_identification(G) == (order(G), 6)
+
+        # [[48, 12, 4]]
+        F = free_group(["r", "s"])
+        r, s = gens(F)
+        G, = quo(F, [r^m, s^2, (r*s)^2])
+        F2G = group_algebra(GF(2), G)
+        r, s = gens(G)
+        a_elts = [one(G), r^3]
+        b_elts = [one(G), s*r^7, r^3, r^4, s*r^10, r^7]
+        c = get_code(a_elts, b_elts, F2G)
+        @test order(G) == 2*m
+        @test describe(G) == "D$(m*2)"
+        @test code_n(c) == 48 && code_k(c) == 12
+        # Oscar.describe(Oscar.small_group(2*m, 6)) is D₂₄, cross-check it with G
+        @test small_group_identification(G) == (order(G), 6)
+
+        # [[48, 16, 3]]
+        F = free_group(["r", "s"])
+        r, s = gens(F)
+        G, = quo(F, [r^m, s^2, (r*s)^2])
+        F2G = group_algebra(GF(2), G)
+        r, s = gens(G)
+        a_elts = [one(G), r^8]
+        b_elts = [one(G), s*r^8, r^9, r^8, s*r^4, r^5]
+        c = get_code(a_elts, b_elts, F2G)
+        @test order(G) == 2*m
+        @test describe(G) == "D$(m*2)"
+        @test code_n(c) == 48 && code_k(c) == 16
+        # Oscar.describe(Oscar.small_group(2*m, 6)) is D₂₄, cross-check it with G
+        @test small_group_identification(G) == (order(G), 6)
+
+        # [[48, 24, 2]]
+        F = free_group(["r", "s"])
+        r, s = gens(F)
+        G, = quo(F, [r^m, s^2, (r*s)^2])
+        F2G = group_algebra(GF(2), G)
+        r, s = gens(G)
+        a_elts = [one(G), r^6]
+        b_elts = [one(G), s*r^11, r^6, s*r^5, r, r^7]
+        c = get_code(a_elts, b_elts, F2G)
+        @test order(G) == 2*m
+        @test describe(G) == "D$(m*2)"
+        @test code_n(c) == 48 && code_k(c) == 24
+        # Oscar.describe(Oscar.small_group(2*m, 6)) is D₂₄, cross-check it with G
+        @test small_group_identification(G) == (order(G), 6)
+
+        # [[56, 8, 7]]
+        m = 14
+        F = free_group(["r", "s"])
+        r, s = gens(F)
+        G, = quo(F, [r^m, s^2, (r*s)^2])
+        F2G = group_algebra(GF(2), G)
+        r, s = gens(G)
+        a_elts = [one(G), r^4]
+        b_elts = [one(G), s*r^11, r^7, s*r^5, r^12, r^9]
+        c = get_code(a_elts, b_elts, F2G)
+        @test order(G) == 2*m
+        @test describe(G) == "D$(m*2)"
+        @test code_n(c) == 56 && code_k(c) == 8
+        # Oscar.describe(Oscar.small_group(2*m, 3)) is D₂₈, cross-check it with G
+        @test small_group_identification(G) == (order(G), 3)
+
+        # [[56, 28, 2]]
+        F = free_group(["r", "s"])
+        r, s = gens(F)
+        G, = quo(F, [r^m, s^2, (r*s)^2])
+        F2G = group_algebra(GF(2), G)
+        r, s = gens(G)
+        a_elts = [one(G), r^7]
+        b_elts = [one(G), s*r^2, r^7, r^8, s*r^9, r]
+        c = get_code(a_elts, b_elts, F2G)
+        @test order(G) == 2*m
+        @test describe(G) == "D$(m*2)"
+        @test code_n(c) == 56 && code_k(c) == 28
+        # Oscar.describe(Oscar.small_group(2*m, 3)) is D₂₈, cross-check it with G
+        @test small_group_identification(G) == (order(G), 3)
+
+        # [[60, 12, 5]]
+        m = 15
+        F = free_group(["r", "s"])
+        r, s = gens(F)
+        G, = quo(F, [r^m, s^2, (r*s)^2])
+        F2G = group_algebra(GF(2), G)
+        r, s = gens(G)
+        a_elts = [one(G), r^12]
+        b_elts = [one(G), s*r^14, r^5, r^12, s*r^11, r^14]
+        c = get_code(a_elts, b_elts, F2G)
+        @test order(G) == 2*m
+        @test describe(G) == "D$(m*2)"
+        @test code_n(c) == 60 && code_k(c) == 12
+        # Oscar.describe(Oscar.small_group(2*m, 3)) is D₃₀, cross-check it with G
+        @test small_group_identification(G) == (order(G), 3)
+
+        # [[60, 20, 3]]
+        F = free_group(["r", "s"])
+        r, s = gens(F)
+        G, = quo(F, [r^m, s^2, (r*s)^2])
+        F2G = group_algebra(GF(2), G)
+        r, s = gens(G)
+        a_elts = [one(G), r^5]
+        b_elts = [one(G), s*r^13, r^5, r^12, s*r^3, r^2]
+        c = get_code(a_elts, b_elts, F2G)
+        @test order(G) == 2*m
+        @test describe(G) == "D$(m*2)"
+        @test code_n(c) == 60 && code_k(c) == 20
+        # Oscar.describe(Oscar.small_group(2*m, 3)) is D₃₀, cross-check it with G
+        @test small_group_identification(G) == (order(G), 3)
+
+        # [[64, 8, 8]]
+        m = 16
+        F = free_group(["r", "s"])
+        r, s = gens(F)
+        G, = quo(F, [r^m, s^2, (r*s)^2])
+        F2G = group_algebra(GF(2), G)
+        r, s = gens(G)
+        a_elts = [one(G), r^6]
+        b_elts = [one(G), s*r^12, s*r^9, r^6, s, s*r]
+        c = get_code(a_elts, b_elts, F2G)
+        @test order(G) == 2*m
+        @test describe(G) == "D$(m*2)"
+        @test code_n(c) == 64 && code_k(c) == 8
+        # Oscar.describe(Oscar.small_group(2*m, 18)) is D₃₂, cross-check it with G
+        @test small_group_identification(G) == (order(G), 18)
+
+        # [[64, 16, 8]]
+        F = free_group(["r", "s"])
+        r, s = gens(F)
+        G, = quo(F, [r^m, s^2, (r*s)^2])
+        F2G = group_algebra(GF(2), G)
+        r, s = gens(G)
+        a_elts = [one(G), r^4]
+        b_elts = [one(G), s*r^10, s*r^3, r^4, s*r^14, s*r^7]
+        c = get_code(a_elts, b_elts, F2G)
+        @test order(G) == 2*m
+        @test describe(G) == "D$(m*2)"
+        @test code_n(c) == 64 && code_k(c) == 16
+        # Oscar.describe(Oscar.small_group(2*m, 18)) is D₃₂, cross-check it with G
+        @test small_group_identification(G) == (order(G), 18)
+
+        # [[64, 32, 2]]
+        F = free_group(["r", "s"])
+        r, s = gens(F)
+        G, = quo(F, [r^m, s^2, (r*s)^2])
+        F2G = group_algebra(GF(2), G)
+        r, s = gens(G)
+        a_elts = [one(G), r^8]
+        b_elts = [one(G), s*r^11, s*r^12, r^8, s*r^3, s*r^4]
+        c = get_code(a_elts, b_elts, F2G)
+        @test order(G) == 2*m
+        @test describe(G) == "D$(m*2)"
+        @test code_n(c) == 64 && code_k(c) == 32
+        # Oscar.describe(Oscar.small_group(2*m, 18)) is D₃₂, cross-check it with G
+        @test small_group_identification(G) == (order(G), 18)
+    end
+end