🐞🦋 fix generation of classical LiftedCode and code_n, code_k parameters

Author: Fe-r-oz

ext/QuantumCliffordHeckeExt/QuantumCliffordHeckeExt.jl

@@ -7,7 +7,7 @@ using DocStringExtensions
 import QuantumClifford, LinearAlgebra
 import Hecke: Group, GroupElem, AdditiveGroupElem,
     GroupAlgebra, GroupAlgebraElem, FqFieldElem, representation_matrix, dim, base_ring,
-    multiplication_table, coefficients, abelian_group, group_algebra, rand
+    multiplication_table, coefficients, abelian_group, group_algebra, rand, order
 import Nemo
 import Nemo: characteristic, matrix_repr, GF, ZZ, lift
 

ext/QuantumCliffordHeckeExt/lifted.jl

@@ -83,7 +83,37 @@ 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 mod l) to the group algebra of the abelian group ℤ/lℤ, with 0 mapped
+to the identity.
+
+# Example
+
+```jldoctest
+julia> base_matrix = [0 0 0 0; 0 1 2 5; 0 6 3 1]; l = 4;
+
+julia> c = LiftedCode(base_matrix, l);
+
+julia> parity_checks(c)
+12×16 Matrix{Bool}:
+ 1  0  0  0  1  0  0  0  1  0  0  0  1  0  0  0
+ 0  1  0  0  0  1  0  0  0  1  0  0  0  1  0  0
+ 0  0  1  0  0  0  1  0  0  0  1  0  0  0  1  0
+ 0  0  0  1  0  0  0  1  0  0  0  1  0  0  0  1
+ 1  0  0  0  0  0  0  1  0  0  1  0  0  0  0  1
+ 0  1  0  0  1  0  0  0  0  0  0  1  1  0  0  0
+ 0  0  1  0  0  1  0  0  1  0  0  0  0  1  0  0
+ 0  0  0  1  0  0  1  0  0  1  0  0  0  0  1  0
+ 1  0  0  0  0  0  1  0  0  1  0  0  0  0  0  1
+ 0  1  0  0  0  0  0  1  0  0  1  0  1  0  0  0
+ 0  0  1  0  1  0  0  0  0  0  0  1  0  1  0  0
+ 0  0  0  1  0  1  0  0  1  0  0  0  0  0  1  0
+
+julia> code_n(c), code_k(c)
+(16, 12)
+```
+"""
 function LiftedCode(shift_array::Matrix{Int}, l::Int; GA::GroupAlgebra=group_algebra(GF(2), abelian_group(l)))
     A = zeros(GA, size(shift_array)...)
     for i in 1:size(shift_array, 1)
@@ -104,9 +134,9 @@ function concat_lift_repr(repr, mat)
 end
 
 function parity_checks(c::LiftedCode)
-    return lift(c.repr, c.A)
+    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))