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tests: Group Presentation for Cyclic Group Cₘₕ = Cₘ × C₂ #398

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Group Presentation for Cyclic Group Cₘₕ = Cₘ × C₂
Fe-r-oz Oct 19, 2024
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Merge branch 'master' into cyclicpresentation
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210 changes: 210 additions & 0 deletions test/test_ecc_2bga_cyclicgroups_presentation.jl
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@testitem "ECC 2BGA Table 2 via Presentation of Cyclic Groups" tags=[:ecc] begin
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@Krastanov Krastanov Dec 31, 2025

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and we have more fine-grained tags now, so that these run on separate test runners

@static if !Sys.iswindows() && Sys.ARCH == :x86_64 && VERSION >= v"1.11"
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@Krastanov Krastanov Dec 31, 2025

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we now have a particular tag that filters tests that require oscar centrally

using JuMP
using HiGHS
using Nemo
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, twobga_from_fp_group
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@Krastanov Krastanov Dec 31, 2025

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two_block_group_algebra_codes is now renamed to singular

using Oscar: free_group, small_group_identification, describe, order, FPGroupElem, FPGroup, FPGroupElem, small_group

@testset "Reproduce Table 2 lin2024quantum" begin
# codes taken from Appendix C, Table 2 of [lin2024quantum](@cite)
# [[16, 2, 4]]
m = 4
F = free_group(["x", "s"])
x, s = gens(F)
G, = quo(F, [x^m, s^2, x * s * x^-1 * s^-1])
F2G = group_algebra(GF(2), G)
x, s = gens(G)
a_elts = [one(G), x]
b_elts = [one(G), x, s, x^2, s*x, s*x^3]
c = twobga_from_fp_group(a_elts, b_elts, F2G)
@test order(G) == 2*m
@test describe(G) == "C$m x C2"
@test code_n(c) == 16 && code_k(c) == 2
@test distance(c, DistanceMIPAlgorithm(solver=HiGHS)) == 4
@test small_group_identification(G) == (order(G), 2)

# [[16, 4, 4]]
b_elts = [one(G), x, s, x^2, s*x, x^3]
c = twobga_from_fp_group(a_elts, b_elts, F2G)
@test order(G) == 2*m
@test describe(G) == "C$m x C2"
@test code_n(c) == 16 && code_k(c) == 4
@test distance(c, DistanceMIPAlgorithm(solver=HiGHS)) == 4
@test small_group_identification(G) == (order(G), 2)

# [[16, 8, 2]]
a_elts = [one(G), s]
b_elts = [one(G), x, s, x^2, s*x, x^2]
c = twobga_from_fp_group(a_elts, b_elts, F2G)
@test order(G) == 2*m
@test describe(G) == "C$m x C2"
@test code_n(c) == 16 && code_k(c) == 8
@test distance(c, DistanceMIPAlgorithm(solver=HiGHS)) == 2
@test small_group_identification(G) == (order(G), 2)

# [[24, 4, 5]]
m = 6
F = free_group(["x", "s"])
x, s = gens(F)
G, = quo(F, [x^m, s^2, x * s * x^-1 * s^-1])
F2G = group_algebra(GF(2), G)
x, s = gens(G)
a_elts = [one(G), x]
b_elts = [one(G), x^3, s, x^4, x^2, s*x]
c = twobga_from_fp_group(a_elts, b_elts, F2G)
@test order(G) == 2*m
@test describe(G) == "C$m x C2"
@test code_n(c) == 24 && code_k(c) == 4
@test distance(c, DistanceMIPAlgorithm(solver=HiGHS)) == 5
@test small_group_identification(G) == (order(G), 5)

# [[24, 12, 2]]
a_elts = [one(G), x^3]
b_elts = [one(G), x^3, s, x^4, s * x^3, x]
c = twobga_from_fp_group(a_elts, b_elts, F2G)
@test order(G) == 2*m
@test describe(G) == "C$m x C2"
@test code_n(c) == 24 && code_k(c) == 12
@test distance(c, DistanceMIPAlgorithm(solver=HiGHS)) == 2
@test small_group_identification(G) == (order(G), 5)

# [[32, 8, 4]]
m = 8
F = free_group(["x", "s"])
x, s = gens(F)
G, = quo(F, [x^m, s^2, x * s * x^-1 * s^-1])
F2G = group_algebra(GF(2), G)
x, s = gens(G)
a_elts = [one(G), x^6]
b_elts = [one(G), s * x^7, s * x^4, x^6, s * x^5, s * x^2]
c = twobga_from_fp_group(a_elts, b_elts, F2G)
@test order(G) == 2*m
@test describe(G) == "C$m x C2"
@test code_n(c) == 32 && code_k(c) == 8
@test distance(c, DistanceMIPAlgorithm(solver=HiGHS)) == 4
@test small_group_identification(G) == (order(G), 5)

# [[32, 16, 2]]
a_elts = [one(G), s * x^4]
b_elts = [one(G), s * x^7, s * x^4, x^6, x^3, s * x^2]
c = twobga_from_fp_group(a_elts, b_elts, F2G)
@test order(G) == 2*m
@test describe(G) == "C$m x C2"
@test code_n(c) == 32 && code_k(c) == 16
@test distance(c, DistanceMIPAlgorithm(solver=HiGHS)) == 2
@test small_group_identification(G) == (order(G), 5)

# [[40, 4, 8]]
m = 10
F = free_group(["x", "s"])
x, s = gens(F)
G, = quo(F, [x^m, s^2, x * s * x^-1 * s^-1])
F2G = group_algebra(GF(2), G)
x, s = gens(G)
a_elts = [one(G), x]
b_elts = [one(G), x^5, x^6, s * x^6, x^7, s * x^3]
c = twobga_from_fp_group(a_elts, b_elts, F2G)
@test order(G) == 2*m
@test describe(G) == "C$m x C2"
@test code_n(c) == 40 && code_k(c) == 4
@test distance(c, DistanceMIPAlgorithm(solver=HiGHS)) == 8
@test small_group_identification(G) == (order(G), 5)

# [[40, 8, 5]]
a_elts = [one(G), x^6]
b_elts = [one(G), x^5, s, x^6 , x, s * x^2]
c = twobga_from_fp_group(a_elts, b_elts, F2G)
@test order(G) == 2*m
@test describe(G) == "C$m x C2"
@test code_n(c) == 40 && code_k(c) == 8
@test distance(c, DistanceMIPAlgorithm(solver=HiGHS)) == 5
@test small_group_identification(G) == (order(G), 5)

# [[40, 20, 2]]
a_elts = [one(G), x^5]
b_elts = [one(G), x^5, s, x^6, s * x^5, x]
c = twobga_from_fp_group(a_elts, b_elts, F2G)
@test order(G) == 2*m
@test describe(G) == "C$m x C2"
@test code_n(c) == 40 && code_k(c) == 20
@test distance(c, DistanceMIPAlgorithm(solver=HiGHS)) == 2
@test small_group_identification(G) == (order(G), 5)

# [[48, 8, 6]]
m = 12
F = free_group(["x", "s"])
x, s = gens(F)
G, = quo(F, [x^m, s^2, x * s * x^-1 * s^-1])
F2G = group_algebra(GF(2), G)
x, s = gens(G)
a_elts = [one(G), s * x^10]
b_elts = [one(G), x^3, s * x^6, x^4, x^7, x^8]
c = twobga_from_fp_group(a_elts, b_elts, F2G)
@test order(G) == 2*m
@test describe(G) == "C$m x C2"
@test code_n(c) == 48 && code_k(c) == 8
@test distance(c, DistanceMIPAlgorithm(solver=HiGHS)) == 6
@test small_group_identification(G) == (order(G), 9)

# [[48, 12, 4]]
a_elts = [one(G), x^3]
b_elts = [one(G), x^3, s * x^6, x^4, s * x^9, x^7]
c = twobga_from_fp_group(a_elts, b_elts, F2G)
@test order(G) == 2*m
@test describe(G) == "C$m x C2"
@test code_n(c) == 48 && code_k(c) == 12
@test distance(c, DistanceMIPAlgorithm(solver=HiGHS)) == 4
@test small_group_identification(G) == (order(G), 9)

# [[48, 16, 3]]
a_elts = [one(G), x^4]
b_elts = [one(G), x^3, s * x^6, x^4, x^7, s * x^10]
c = twobga_from_fp_group(a_elts, b_elts, F2G)
@test order(G) == 2*m
@test describe(G) == "C$m x C2"
@test code_n(c) == 48 && code_k(c) == 16
@test distance(c, DistanceMIPAlgorithm(solver=HiGHS)) == 3
@test small_group_identification(G) == (order(G), 9)

# [[48, 24, 2]]
a_elts = [one(G), s * x^6]
b_elts = [one(G), x^3, s * x^6, x^4, s * x^9, s * x^10]
c = twobga_from_fp_group(a_elts, b_elts, F2G)
@test order(G) == 2*m
@test describe(G) == "C12 x C2"
@test code_n(c) == 48 && code_k(c) == 24
@test distance(c, DistanceMIPAlgorithm(solver=HiGHS)) == 2
@test small_group_identification(G) == (order(G), 9)

# [[56, 8, 7]]
m = 14
F = free_group(["x", "s"])
x, s = gens(F)
G, = quo(F, [x^m, s^2, x * s * x^-1 * s^-1])
F2G = group_algebra(GF(2), G)
x, s = gens(G)
a_elts = [one(G), x^8]
b_elts = [one(G), x^7, s, x^8, x^9, s * x^4]
c = twobga_from_fp_group(a_elts, b_elts, F2G)
@test order(G) == 2*m
@test describe(G) == "C$m x C2"
@test code_n(c) == 56 && code_k(c) == 8
@test distance(c, DistanceMIPAlgorithm(solver=HiGHS)) == 7
@test small_group_identification(G) == (order(G), 4)

# [[56, 28, 2]]
a_elts = [one(G), x^7]
b_elts = [one(G), x^7, s, x^8, s * x^7, x]
c = twobga_from_fp_group(a_elts, b_elts, F2G)
@test order(G) == 2*m
@test describe(G) == "C$m x C2"
@test code_n(c) == 56 && code_k(c) == 28
@test distance(c, DistanceMIPAlgorithm(solver=HiGHS)) == 2
@test small_group_identification(G) == (order(G), 4)
end
end
end
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