doctests for CSS and non-CSS HyperBicycleCode

Author: Fe-r-oz

src/Quantum/product_codes.jl

@@ -176,6 +176,31 @@ Return the hyperbicycle CSS code of `a` and `b` given `χ`.
 - b: A vector of length `c` of binary matrices of the same dimensions,
   potentially different from those of `a`.
 - χ: A strictly positive integer coprime with `c`.
+
+# Example
+
+[[900, 50, 14]] CSS Hyperbicycle Code from Example 6 of [Kovalev_2013](@cite).
+
+```jldoctest
+julia> S, x = polynomial_ring(Oscar.Nemo.Native.GF(2), :x);
+
+julia> l = 30; χ = 1;
+
+julia> R, = residue_ring(S, x^l - 1);
+
+julia> h = R(1 + x + x^3 + x^5);
+
+julia> A = residue_polynomial_to_circulant_matrix(h);
+
+julia> a1 = A[1:15, 1:15];
+
+julia> a2 = A[1:15, 16:30];
+
+julia> code = HyperBicycleCodeCSS([a1, a2], [a1, a2], χ);
+
+julia> length(code), dimension(code)
+(900, 50)
+```
 """
 function HyperBicycleCodeCSS(a::Vector{T}, b::Vector{T}, χ::Int; char_vec::Union{Vector{zzModRingElem},
     Missing} = missing, logs_alg::Symbol = :stnd_frm) where T <: CTMatrixTypes
@@ -232,6 +257,29 @@ Return the hyperbicycle non-CSS code of `a` and `b` given `χ`.
 - b: A vector of length `c` of binary matrices of the same dimensions,
   potentially different from those of `a`.
 - χ: A strictly positive integer coprime with `c`.
+
+# Example
+
+[[289, 81, 5]] non-CSS Hyperbicycle Code from Example 13 of [Kovalev_2013](@cite).
+
+```jldoctest
+julia> using CodingTheory, Oscar;
+
+julia> S, x = polynomial_ring(Oscar.Nemo.Native.GF(2), :x);
+
+julia> l = 17; χ = 1;
+
+julia> R, = residue_ring(S, x^l - 1);
+
+julia> h = R(x^4 * (1 + x + x^3 + x^6 + x^8 + x^9));
+
+julia> A = residue_polynomial_to_circulant_matrix(h);
+
+julia> code = HyperBicycleCode([A], [A], χ);
+
+julia> length(code), dimension(code)
+(289, 81)
+```
 """
 function HyperBicycleCode(a::Vector{T}, b::Vector{T}, χ::Int, char_vec::Union{Vector{zzModRingElem},
     Missing} = missing, logs_alg::Symbol = :stnd_frm) where T <: CTMatrixTypes