introducing non-abelian groups via Hecke's small group with multiplication table

Author: Fe-r-oz

ext/QuantumCliffordHeckeExt/QuantumCliffordHeckeExt.jl

@@ -5,7 +5,7 @@ using DocStringExtensions
 import QuantumClifford, LinearAlgebra
 import Hecke: Group, GroupElem, AdditiveGroup, AdditiveGroupElem,
     GroupAlgebra, GroupAlgebraElem, FqFieldElem, representation_matrix, dim, base_ring,
-    multiplication_table, coefficients, abelian_group, group_algebra
+    multiplication_table, coefficients, abelian_group, group_algebra, small_group, direct_product
 import Nemo
 import Nemo: characteristic, matrix_repr, GF, ZZ, lift
 

ext/QuantumCliffordHeckeExt/lifted_product.jl

@@ -150,6 +150,17 @@ function two_block_group_algebra_codes(a::GroupAlgebraElem, b::GroupAlgebraElem)
     LPCode(A, B)
 end
 
+function two_block_group_algebra_codes(a_shifts::Array{Int}, b_shifts::Array{Int}, sg1::Tuple{Int,Int}, sg2::Tuple{Int,Int})
+    m, i = sg1
+    l, i = sg2
+    g1 = small_group(m, i)
+    g2 = small_group(l, i)
+    GA = group_algebra(GF(2), direct_product(g1, g2))
+    a = sum(GA[n%dim(GA)+1] for n in a_shifts)
+    b = sum(GA[n%dim(GA)+1] for n in b_shifts)
+    two_block_group_algebra_codes(a, b)
+end
+
 """
 Generalized bicycle codes, which are a special case of 2GBA codes (and therefore of lifted product codes).
 Here the group is chosen as the cyclic group of order `l`,