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Coprime Bivariate Bicycle code via Hecke's Group Algebra #378
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I think the PR is ready for review. Thank you! |
Codecov ReportAll modified and coverable lines are covered by tests ✅
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Misses 777 777 ☔ View full report in Codecov by Sentry. |
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. |
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This is wonderful, thank you! I think it would make sense to put the docstring in a different location though (see comments below)
# 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).
@@ -0,0 +1,59 @@ | |||
@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
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.