Haah's cubic code using abelian group ℤ₃ˣ³ via Hecke's Group Algebra

[Fe-r-oz]

This PR aims to implement Haah's cubic code, a cousin of Generalized Bicycle code as mentioned in https://errorcorrectionzoo.org/c/generalized_bicycle.

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[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 83.01%. Comparing base (2b8e81f) to head (86e622f).

Additional details and impacted files

@@            Coverage Diff             @@
##           master     #388      +/-   ##
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- Coverage   83.03%   83.01%   -0.03%     
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  Files          70       70              
  Lines        4404     4409       +5     
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+ Hits         3657     3660       +3     
- Misses        747      749       +2     

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[Fe-r-oz]

I think this is ready for review, @Krastanov. Thanks!

Brief context: For GB codes , n%l+1 is used for GroupAlgebra (GA) indexing to indicate the cyclic nature for single cyclic group. This is same as doing n%dim(GA)+1. This works as here, we have a single cyclic group of order l, so total order is l which can be acquired using dim(GA).

In Haah cubic code case, the total order is l³, hence using n%dim(GA)+1 is appropriate since dim(GA) would give l³ because here, direct product of three cyclic groups ( total order = lxlxl) is the requirement. Also, The CI errors are unrelated to this PR.

Edit:

For large values of l, there are some crashes due to huge cubic lattice, GA with sparse representation is being worked on by Tommy here: thofma/Hecke.jl#1655. I will add this functionality once available.