Coprime Bivariate Bicycle code via Hecke's Group Algebra #378
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Fe-r-oz
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I think the PR is ready for review. Thank you! |
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Codecov ReportAll modified and coverable lines are covered by tests ✅
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Since #394 is fixed, I can now add the tests that reproduce all the results from Table 2 for these codes. I waited because otherwise, it would have caused CI failures. |
Fe-r-oz
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| # Examples | ||
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| The coprime bivariate bicycle (BB) codes are defined by two polynomials `𝑎(𝑥,𝑦)` and `𝑏(𝑥,𝑦)`, | ||
| where `𝑙` and `𝑚` are coprime, and can be expressed as univariate polynomials `𝑎(𝜋)` and `𝑏(𝜋)`, | ||
| with generator `𝜋 = 𝑥𝑦`. They can be viewed as a special case of Lifted Product construction | ||
| based on abelian group `ℤₗ x ℤₘ` where `ℤⱼ` cyclic group of order `j`. | ||
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| [108, 12, 6]] coprime-bivariate bicycle (BB) code from Table 2 of [wang2024coprime](@cite). | ||
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| ```jldoctest | ||
| julia> import Hecke: group_algebra, GF, abelian_group, gens; | ||
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| julia> l=2; m=27; | ||
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| julia> GA = group_algebra(GF(2), abelian_group([l*m])); | ||
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| julia> 𝜋 = gens(GA)[1]; | ||
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| julia> A = reshape([𝜋^2 + 𝜋^5 + 𝜋^44], (1,1)); | ||
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| julia> B = reshape([𝜋^8 + 𝜋^14 + 𝜋^47], (1,1)); | ||
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| julia> c = LPCode(A, B); | ||
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| julia> code_n(c), code_k(c) | ||
| (108, 12) | ||
| ``` |
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This seems like an example of a two_block_group_algebra_codes so it should probably go in its docstring, not here, next to the other example you have already given (that I merged earlier today, so presumably this also needs a merge with master to avoid a merge conflict).
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| @testitem "ECC coprime Bivaraite Bicycle" begin | |||
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very useful set of tests! It should probably directly use two_block_group_algebra_code instead of the more round-about construction with LPCode
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Thank you for your suggestions! Incorporated all of your comments and added coprimeBB codes in This PR is ready for review, Thank you! |
This PR aims to introduce an easy construction method for coprime bivaraite bicycle codes using lifted product
LPCode, and OscarSubPcGroup. The code_n and code_k parameters match exactly from the Table 2, Section 5 of Coprime Bivariate Bicycle Codes and their Properties.