Tetravariate Tetracycle Code

[Fe-r-oz]

This PR implements a novel quantum error correcting code family, namely Tetravariate Tetracycle Code which supports full single shot decoding since it's provides both metacheck matrices, $M_X$ and $M_Z$. The limitation of the Trivariate Tricycle code #583 is that it supports partial single shot decoding.

Here is the novel [[648, 18, d]] tetravariate tetracycle code.

julia> using Oscar; using QuantumClifford.ECC;

julia> l, m, p, r = 4, 3, 3, 3;

julia> R, (w, x, y, z) = polynomial_ring(GF(2), [:w, :x, :y, :z]);

julia> I = ideal(R, [w^l - 1, x^m - 1, y^p - 1, z^r - 1]);

julia> S, _ = quo(R, I);

julia> A = S((1 + x^2 )*(1 + w*x*y*z^2));

julia> B = S((1 + x^2)*(1 + w*x^3*y^2*z));

julia> C = S(1 + w^2*x^2*y^2*z^2);

julia> D = S(1 + w^3*x^3*y^3*z^3);

julia> c = TetravariateTetracycleCode(l, m, p, r, A, B, C, D);

julia> code_n(c), code_k(c)
(648, 18)

• The code is properly formatted and commented.
• Substantial new functionality is documented within the docs.
• All new functionality is tested.
• All of the automated tests on github pass.
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[codecov]

Codecov Report

❌ Patch coverage is 91.42857% with 6 lines in your changes missing coverage. Please review.
✅ Project coverage is 76.63%. Comparing base (73c133a) to head (53c8031).

Files with missing lines	Patch %	Lines
...QuantumCliffordOscarExt/tetravariate_tetracycle.jl	92.30%	5 Missing ⚠️
src/ecc/codes/qeccs_using_oscar.jl	80.00%	1 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master     #590      +/-   ##
==========================================
+ Coverage   76.53%   76.63%   +0.09%     
==========================================
  Files         122      123       +1     
  Lines        7491     7561      +70     
==========================================
+ Hits         5733     5794      +61     
- Misses       1758     1767       +9     

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