add doctests for gaugeShorcode

Author: Fe-r-oz

docs/src/references.bib

@@ -109,6 +109,17 @@ @misc{Vasmer_2020
   year={2020}
 }
 
+@article{poulin2005stabilizer,
+  title={Stabilizer formalism for operator quantum error correction},
+  author={Poulin, David},
+  journal={Physical review letters},
+  volume={95},
+  number={23},
+  pages={230504},
+  year={2005},
+  publisher={APS}
+}
+
 % Product Codes
 
 @article{bacon2006quantum,

src/Quantum/misc_known_codes.jl

@@ -8,6 +8,46 @@
       # Subsystem codes
 #############################
 
+"""
+[[9, 1, 4, 3]] gauged Shor code from [poulin2005stabilizer](@cite)
+
+```jldoctest
+julia> using CodingTheory, Oscar;
+
+julia> code = GaugedShorCode();
+
+julia> length(code), dimension(code), code.r
+(9, 1, 4)
+
+julia> code.stabs_stand
+[1   0   1   1   1   1   1   0   0   0   0   0   0   0   0   0   0   0]
+[0   1   0   0   1   1   1   1   1   0   0   0   0   0   0   0   0   0]
+[0   0   0   0   0   0   0   0   0   1   1   1   0   1   0   1   1   0]
+[0   0   0   0   0   0   0   0   0   1   0   0   1   1   1   0   1   1]
+
+julia> code.logicals
+1-element Vector{Tuple{fpMatrix, fpMatrix}}:
+ ([0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1], [1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0])
+
+julia> code.X_stabs
+[1   1   1   1   1   1   0   0   0]
+[1   1   1   0   0   0   1   1   1]
+
+julia> code.Z_stabs
+[1   1   0   1   1   0   1   1   0]
+[0   1   1   0   1   1   0   1   1]
+
+julia> code.g_ops_mat
+[0   0   0   0   0   0   0   0   0   0   1   1   0   0   0   0   0   0]
+[0   0   1   0   0   0   0   0   1   0   0   0   0   0   0   0   0   0]
+[0   0   0   0   0   0   0   0   0   0   0   0   0   1   1   0   0   0]
+[0   0   0   0   0   1   0   0   1   0   0   0   0   0   0   0   0   0]
+[0   0   0   0   0   0   0   0   0   1   1   0   0   0   0   0   0   0]
+[1   0   0   0   0   0   1   0   0   0   0   0   0   0   0   0   0   0]
+[0   0   0   0   0   0   0   0   0   0   0   0   1   1   0   0   0   0]
+[0   0   0   1   0   0   1   0   0   0   0   0   0   0   0   0   0   0]
+```
+"""
 function GaugedShorCode()
     # Poulin, "Stabilizer Formalism for Operator Quantum Error Correction", (2008)
     # [[9, 1, 4, 3]] gauged Shor code

src/Quantum/product_codes.jl

@@ -666,7 +666,7 @@ julia> R, _ = residue_ring(S, x^l - 1);
 julia> A1 = matrix(R, 1, 1, [1 + x^1 + x^6]);
 
 julia> A2 = matrix(R, 7, 7,
-           [x^36, 0   , 0   , 0   , 0   , 1   , x^9,
+           [x^36, 0   , 0   , 0   , 0   , 1   , x^9 ,
             x^9 , x^36, 0   , 0   , 0   , 0   , 1   ,
             1   , x^9 , x^36, 0   , 0   , 0   , 0   ,
             0   , 1   , x^9 , x^36, 0   , 0   , 0   ,

test/Quantum/product_codes_test.jl

@@ -670,12 +670,13 @@
 
     @testset "BiasTailoredLiftedProductCode" begin
         # [[882, 24, d ≤ 24]] from Appendix B of https://arxiv.org/pdf/2202.01702
+        F = Oscar.Nemo.Native.GF(2)
         S, x = polynomial_ring(F, :x)
         l = 63
         R, _ = residue_ring(S, x^l - 1)
         A1 = matrix(R, 1, 1, [1 + x^1 + x^6])
         A2 = matrix(R, 7, 7,
-             [x^36, 0   , 0   , 0   , 0   , 1   , x^9,
+             [x^36, 0   , 0   , 0   , 0   , 1   , x^9 ,
               x^9 , x^36, 0   , 0   , 0   , 0   , 1   ,
               1   , x^9 , x^36, 0   , 0   , 0   , 0   ,
               0   , 1   , x^9 , x^36, 0   , 0   , 0   ,