Multivariate Bicycle code via Hecke's Group Algebra

[Fe-r-oz]

This PR implements all the Multivariate Bicycle (MB) using Lifted Product construction and use of Oscar Product of Groups from the paper Multivariate Bicycle Codes. All the MB code constructions from Appendix A Table 2 can be verified using the construction method presented.

Many thanks to Sim J. Xian for clarifying something explicitly, it was an important detail about construction which seemed to be missing from their paper since they only mentioned order l and m, for two cyclic groups. That third generator is z=xy . I was wondering for some time the order of the third cyclic group for the codes to be MB code: 𝐺ᵣ = ℤ/l₁ × ℤ/l₂ × ℤ/l₃ as only l and m, order of first two cyclic groups, were mentioned in their paper explicitly.

With z=xy, the codes can be constructed with correct code_n and code_k parameters.

I have added doctests for Weight-7 and Weight-6 MB codes, which give correct results for code_n and code_k values.

• 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.

[Fe-r-oz]

I think the PR is ready for review. Thank you!

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 83.06%. Comparing base (be50f9c) to head (66e4891).

Additional details and impacted files

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  Coverage   83.06%   83.06%           
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  Files          70       70           
  Lines        4410     4410           
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  Hits         3663     3663           
  Misses        747      747           

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[Fe-r-oz]

Since #394 is fixed, added the tests that reproduce all the results from Table 1 for these codes.