fix parity_matrix generation and parameter calculations in classical LiftedCode

ext/QuantumCliffordHeckeExt/QuantumCliffordHeckeExt.jl

@@ -4,25 +4,24 @@ using QECCore
 import QECCore: code_n, code_s, code_k, rate, distance
 using DocStringExtensions
 
-import QuantumClifford
-import QuantumClifford: gf2_row_echelon_with_pivots!
-import LinearAlgebra
+import QuantumClifford, LinearAlgebra
+
 import Hecke: Group, GroupElem, AdditiveGroupElem,
     GroupAlgebra, GroupAlgebraElem, FqFieldElem, representation_matrix, dim, base_ring,
     multiplication_table, coefficients, abelian_group, group_algebra, rand, gens, order,
     is_commutative, FqPolyRingElem, residue_ring, coeff, zero_matrix, mod1, lift, ZZ, gen,
-    matrix, ncols, nrows, degree, EuclideanRingResidueRingElem, quo, parent, zero, gcd,
-    polynomial_ring, characteristic, isone, mod, factor, zeros
+    polynomial_ring, characteristic, isone, mod, factor, zeros, group, EuclideanRingResidueRingElem,
+    degree, gcd, nrows, ncols
 import Hecke.Generic.MatSpaceElem
 import Nemo
-import Nemo: characteristic, matrix_repr, GF, ZZ, lift, rank
+import Nemo: characteristic, matrix_repr, GF, ZZ, lift, matrix, rank
 
-import QuantumClifford.ECC: iscss, parity_checks,
+import QuantumClifford.ECC: iscss, parity_checks, parity_matrix,
     two_block_group_algebra_codes, generalized_bicycle_codes, bicycle_codes, check_repr_commutation_relation,
     haah_cubic_codes, honeycomb_color_codes, check_repr_regular_linear, random_qc_ghp_code_matrix_A
 
 import QECCore: AbstractQECC, CSS, AbstractCSSCode,
-    hgp, code_k, code_n, code_s, parity_matrix_x, parity_matrix_z, parity_matrix_xz
+    hgp, code_k, code_n, code_s, parity_matrix_x, parity_matrix_z, parity_matrix_xz, parity_matrix
 
 import Random
 import Random: AbstractRNG, default_rng, randperm

ext/QuantumCliffordHeckeExt/lifted.jl

@@ -70,7 +70,44 @@ function LiftedCode(A::Matrix{GroupAlgebraElem{FqFieldElem, <: GroupAlgebra}}; G
     LiftedCode(A; GA=GA, repr=representation_matrix)
 end
 
-# TODO document and doctest example
+"""
+Constructs a group algebra code by embedding a matrix of group elements into the
+specified group algebra `GA`, with optional custom representation  `repr`.
+
+# Example
+
+```jldoctest
+julia> import Hecke: group_algebra, GF, abelian_group, gens, representation_matrix
+
+julia> import QuantumClifford.ECC: LiftedCode, code_n, code_k, code_s
+
+julia> import QuantumClifford.ECC.QECCore: parity_matrix
+
+julia> l = 12; GA = group_algebra(GF(2), abelian_group(l)); x = gens(GA)[];
+
+julia> B = reshape([1 + x + x^3 + x^6], (1, 1));
+
+julia> c = LiftedCode(B, repr = representation_matrix);
+
+julia> code = parity_matrix(c)
+12×12 Matrix{Bool}:
+ 1  0  0  0  0  0  1  0  0  1  0  1
+ 1  1  0  0  0  0  0  1  0  0  1  0
+ 0  1  1  0  0  0  0  0  1  0  0  1
+ 1  0  1  1  0  0  0  0  0  1  0  0
+ 0  1  0  1  1  0  0  0  0  0  1  0
+ 0  0  1  0  1  1  0  0  0  0  0  1
+ 1  0  0  1  0  1  1  0  0  0  0  0
+ 0  1  0  0  1  0  1  1  0  0  0  0
+ 0  0  1  0  0  1  0  1  1  0  0  0
+ 0  0  0  1  0  0  1  0  1  1  0  0
+ 0  0  0  0  1  0  0  1  0  1  1  0
+ 0  0  0  0  0  1  0  0  1  0  1  1
+
+julia> code_n(c), code_k(c), code_s(c)
+(12, 3, 12)
+```
+"""
 function LiftedCode(group_elem_array::Matrix{<: GroupOrAdditiveGroupElem}; GA::GroupAlgebra=group_algebra(GF(2), parent(group_elem_array[1,1])), repr::Union{Function, Nothing}=nothing)
     A = zeros(GA, size(group_elem_array)...)
     for i in axes(group_elem_array, 1), j in axes(group_elem_array, 2)
@@ -83,7 +120,37 @@ function LiftedCode(group_elem_array::Matrix{<: GroupOrAdditiveGroupElem}; GA::G
     end
 end
 
-# TODO document and doctest example
+"""
+Constructs a group algebra code over `GF(2)` by lifting a matrix of cyclic shifts
+(entries modulo `l`)  to the group algebra of the abelian group `ℤ/lℤ` of order `l`.
+
+# Example
+
+```jldoctest
+julia> import Hecke; import QuantumClifford.ECC: LiftedCode, code_n, code_k, code_s
+
+julia> import QuantumClifford.ECC.QECCore: parity_matrix
+
+julia> base_matrix = [0 0 0 0; 0 1 2 5; 0 6 3 1]; l = 3;
+
+julia> c = LiftedCode(base_matrix, l);
+
+julia> code = parity_matrix(c)
+9×12 Matrix{Bool}:
+ 1  0  0  1  0  0  1  0  0  1  0  0
+ 0  1  0  0  1  0  0  1  0  0  1  0
+ 0  0  1  0  0  1  0  0  1  0  0  1
+ 1  0  0  0  0  1  0  1  0  0  1  0
+ 0  1  0  1  0  0  0  0  1  0  0  1
+ 0  0  1  0  1  0  1  0  0  1  0  0
+ 1  0  0  1  0  0  1  0  0  0  0  1
+ 0  1  0  0  1  0  0  1  0  1  0  0
+ 0  0  1  0  0  1  0  0  1  0  1  0
+
+julia> code_n(c), code_k(c), code_s(c)
+(12, 5, 9)
+```
+"""
 function LiftedCode(shift_array::Matrix{Int}, l::Int; GA::GroupAlgebra=group_algebra(GF(2), abelian_group(l)), repr=representation_matrix)
     A = zeros(GA, size(shift_array)...)
     for i in 1:size(shift_array, 1)
@@ -103,10 +170,10 @@ function concat_lift_repr(repr, mat)
     return z
 end
 
-function parity_checks(c::LiftedCode)
-    return lift(c.repr, c.A)
+function parity_matrix(c::LiftedCode)
+    return concat_lift_repr(c.repr, c.A)
 end
 
-code_n(c::LiftedCode) = size(c.A, 2) * size(zero(c.GA), 2)
+code_n(c::LiftedCode) = size(c.A, 2) * order(group(c.GA))
 
-code_s(c::LiftedCode) = size(c.A, 1) * size(zero(c.GA), 1)
+code_s(c::LiftedCode) = size(c.A, 1) * order(group(c.GA))

ext/QuantumCliffordOscarExt/bivariate_bicycle.jl

@@ -25,7 +25,7 @@ We consider the specific ideal generated by two polynomials enforcing periodic b
 
 ```math
 \\begin{aligned}
-J = \\langle x^\\ell - 1, y^m - 1 \\rangle = { p(x,y)(x^\ell - 1) + q(x,y)(y^m - 1) \\mid p, q \\in \\mathbb{F}_2[x,y]}
+J = \\langle x^\\ell - 1, y^m - 1 \\rangle = { p(x,y)(x^\\ell - 1) + q(x,y)(y^m - 1) \\mid p, q \\in \\mathbb{F}_2[x,y]}
 \\end{aligned}
 ```
 
@@ -37,7 +37,7 @@ conditions in the y-direction.
 
 Formally, to verify that ``J`` satisfies the *ideal* requirements, the properties of J are as follows:
 
-- ``(J, +) \\leq mathbb{F}_2[x, y], +)``
+- ``(J, +) \\leq \\mathbb{F}_2[x, y], +)``
 
 For any ``f(x,y) \\in \\mathbb{F}_2[x, y]`` and any ``j(x,y) \\in J``:
 - ``f(x,y) \\cdot j(x,y) \\in J``

test/test_cecc.jl

@@ -1,5 +1,6 @@
 @testitem "ECC" tags=[:ecc, :ecc_base] begin
     using Nemo
+    using Hecke
     using QuantumClifford.ECC
     using QuantumClifford.ECC: AbstractCECC, QECCore
 

test/test_cecc_base.jl

@@ -7,6 +7,7 @@ using InteractiveUtils
 using SparseArrays
 
 import Nemo: GF, matrix, rank, finite_field, polynomial_ring
+import Hecke: group_algebra, abelian_group, gens, representation_matrix
 import LinearAlgebra
 
 include("test_ecc_base.jl")
@@ -40,6 +41,13 @@ R, z = polynomial_ring(F, :z)
 g₄ = z^2 + α^7*z + 1
 L₄ = [α^i for i in 2:13]
 
+# Lifted Codes
+l₁ = 12; GA₁ = group_algebra(GF(2), abelian_group(l)); x = gens(GA)[]
+B₁ = reshape([1 + x + x^3 + x^6], (1, 1))
+c = LiftedCode(B, repr = representation_matrix)
+
+base_matrix₂ = [0 0 0 0; 0 1 2 5; 0 6 3 1]; l₂ = 3;
+
 const classical_code_instance_args = Dict(
     :RepCode => [3, 4, 5, 6, 7, 8, 9, 10],
     :BCH => [(3, 1), (3, 2), (4, 1), (4, 1), (5, 1), (5, 2), (6, 1), (6, 2)],
@@ -48,7 +56,8 @@ const classical_code_instance_args = Dict(
     :Golay => [(23), (24)],
     :Hamming => [2, 3, 4, 5, 6, 7, 8],
     :GallagerLDPC => [(3, 3, 4), (3, 4, 5), (4, 5, 7), (4, 6, 7)],
-    :GoppaCode => [(m₁, t₁, g₁, L₁), (m₂, t₂, g₂), (m₃, t₃, g₃), (m₄, t₄, g₄, L₄)]
+    :GoppaCode => [(m₁, t₁, g₁, L₁), (m₂, t₂, g₂), (m₃, t₃, g₃), (m₄, t₄, g₄, L₄)],
+    :LiftedCode => [(B₁, repr = representation_matrix), (base_matrix₂, l₂), (base_matrix₂, 5), (base_matrix₂, 7)]
 )
 
 function all_testable_classical_code_instances(; maxn=nothing)

test/test_ecc_throws.jl

@@ -1,6 +1,8 @@
 @testitem "ECC throws" tags=[:ecc, :ecc_base] begin
 
-    using QuantumClifford.ECC: ReedMuller, BCH, RecursiveReedMuller, Golay, Triangular488, Triangular666, Hamming
+    using Hecke
+    using Hecke: group_algebra, GF, abelian_group, gens, one, representation_matrix
+    using QuantumClifford.ECC: ReedMuller, BCH, RecursiveReedMuller, Golay, Triangular488, Triangular666, Hamming, LiftedCode, code_k, code_n, code_s, parity_matrix
 
     @test_throws ArgumentError ReedMuller(-1, 3)
     @test_throws ArgumentError ReedMuller(1, 0)
@@ -26,4 +28,18 @@
     @test_throws ArgumentError Triangular488(1)
     @test_throws ArgumentError Triangular666(8)
     @test_throws ArgumentError Triangular666(1)
+
+    l = 12; GA = group_algebra(GF(2), abelian_group(l)); x = gens(GA)[]
+    B = reshape([1 + x + x^3 + x^6], (1, 1))
+    c = LiftedCode(B, repr = representation_matrix)
+    @test_nowarn parity_matrix(c)
+    @test_nowarn code_n(c)
+    @test_nowarn code_k(c)
+    @test_nowarn code_s(c)
+    base_matrix = [0 0 0 0; 0 1 2 5; 0 6 3 1]; l = 3;
+    c = LiftedCode(base_matrix, l);
+    @test_nowarn parity_matrix(c)
+    @test_nowarn code_n(c)
+    @test_nowarn code_k(c)
+    @test_nowarn code_s(c)
 end