InterleavedCode proofs #143
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Thank you! Hoping to review these tomorrow and merge. |
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@quangvdao Is there any reason why the definition of LawfulInterleavedCode is weaker than the one in the Ligero paper? Namely, they define interleaved codes to have MF=matrixSubmoduleOfLinearCode κ LC (in line with codeOfLinearCode). It seems that the results become much harder (or impossible) to prove for the current definition. |
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winger
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Added proofs for the rest of the theorems in InterleavedCode.lean |
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Hi @winger, thanks for your comments! Which definition exactly did you have an objection to so I can take a look? |
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Proofs for:
lemma minDist_eq_minDist [ArkLib/Data/CodingTheory/InterleavedCode.lean] #112
Note: this is the proof for corrected statement, the original version only holds as an inequality (see the proof baseMinDist_le_minDist_of_nontrivialMF for inequality and a counterexample in GeneralInequalityAndCounterexample section)
lemma isInterleaved_codeOfLinearCode [ArkLib/Data/CodingTheory/InterleavedCode.lean] #111