add missing method for two-block group algebra (2BGA) codes

Author: Fe-r-oz

docs/src/references.bib

@@ -487,3 +487,14 @@ @article{anderson2014fault
   year={2014},
   publisher={APS}
 }
+
+@article{lin2024quantum,
+  title={Quantum two-block group algebra codes},
+  author={Lin, Hsiang-Ku and Pryadko, Leonid P},
+  journal={Physical Review A},
+  volume={109},
+  number={2},
+  pages={022407},
+  year={2024},
+  publisher={APS}
+}

docs/src/references.md

@@ -40,6 +40,7 @@ For quantum code construction routines:
 - [steane1999quantum](@cite)
 - [campbell2012magic](@cite)
 - [anderson2014fault](@cite)
+- [lin2024quantum](@cite)
 
 For classical code construction routines:
 - [muller1954application](@cite)

ext/QuantumCliffordHeckeExt/lifted_product.jl

@@ -139,19 +139,38 @@ code_n(c::LPCode) = size(c.repr(zero(c.GA)), 2) * (size(c.A, 2) * size(c.B, 1) +
 code_s(c::LPCode) = size(c.repr(zero(c.GA)), 1) * (size(c.A, 1) * size(c.B, 1) + size(c.A, 2) * size(c.B, 2))
 
 """
-Two-block group algebra (2GBA) codes, which are a special case of lifted product codes
+Two-block group algebra (2BGA) codes, which are a special case of lifted product codes
 from two group algebra elements `a` and `b`, used as `1x1` base matrices.
 
+[[70, 8, 10]] 2BGA code from Table 1 of [lin2024quantum](@cite) with cyclic group of
+order `l = 35`.
+
+```jldoctest
+julia> l = 35;
+
+julia> c1 = two_block_group_algebra_codes([0, 15, 16, 18], [0, 1, 24, 27], l);
+
+julia> code_n(c1), code_k(c1)
+(70, 8)
+```
+
 See also: [`LPCode`](@ref), [`generalized_bicycle_codes`](@ref), [`bicycle_codes`](@ref)
-""" # TODO doctest example
+"""
 function two_block_group_algebra_codes(a::GroupAlgebraElem, b::GroupAlgebraElem)
     A = reshape([a], (1, 1))
     B = reshape([b], (1, 1))
     LPCode(A, B)
 end
 
+function two_block_group_algebra_codes(a_shifts::Array{Int}, b_shifts::Array{Int}, l::Int)
+    GA = group_algebra(GF(2), abelian_group(l))
+    a = sum(GA[n%l+1] for n in a_shifts)
+    b = sum(GA[n%l+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).
+Generalized bicycle codes, which are a special case of 2BGA codes (and therefore of lifted product codes).
 Here the group is chosen as the cyclic group of order `l`,
 and the base matrices `a` and `b` are the sum of the group algebra elements corresponding to the shifts `a_shifts` and `b_shifts`.
 

test/test_ecc_2bga.jl

@@ -0,0 +1,16 @@
+@testitem "ECC 2BGA" begin
+    using Hecke
+    using QuantumClifford.ECC: two_block_group_algebra_codes, code_k, code_n
+
+    # codes taken from Table 1 of [lin2024quantum](@cite)
+    @test code_n(two_block_group_algebra_codes([0 , 15, 16, 18], [0 ,  1, 24, 27], 35)) == 70
+    @test code_k(two_block_group_algebra_codes([0 , 15, 16, 18], [0 ,  1, 24, 27], 35)) == 8
+    @test code_n(two_block_group_algebra_codes([0 ,  1,  3,  7], [0 ,  1, 12, 19], 27)) == 54
+    @test code_k(two_block_group_algebra_codes([0 ,  1,  3,  7], [0 ,  1, 12, 19], 27)) == 6
+    @test code_n(two_block_group_algebra_codes([0 , 10,  6, 13], [0 , 25, 16, 12], 30)) == 60
+    @test code_k(two_block_group_algebra_codes([0 , 10,  6, 13], [0 , 25, 16, 12], 30)) == 6
+    @test code_n(two_block_group_algebra_codes([0 ,  9, 28, 31], [0 ,  1, 21, 34], 36)) == 72
+    @test code_k(two_block_group_algebra_codes([0 ,  9, 28, 31], [0 ,  1, 21, 34], 36)) == 8
+    @test code_n(two_block_group_algebra_codes([0 ,  9, 28, 13], [0 ,  1, 21, 34], 36)) == 72
+    @test code_k(two_block_group_algebra_codes([0 ,  9, 28, 13], [0 ,  1,  3, 22], 36)) == 10
+end