Chain of Separable Binary Goppa Codes and their Minimal Distance

2007/07/27 by Sergey Bezzateev, Bezzateev, Sergey, Natalia Shekhunova +1 · 2 citations
Biochemistry, Genetics and Molecular Biology · Computer Science · Engineering · Mathematics · #Coding theory and cryptography #DNA and Biological Computing #E.4.x #FOS: Computer and information sciences #Information Theory (cs.IT) #cs.IT #graph theory and CDMA systems #math.IT

paper · pdf · doi:10.48550/arxiv.0707.4083

7 pages, 1 figure

arxiv created 2007/07/27 · openalex publication_date 2007/07/27 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

It is shown that subclasses of separable binary Goppa codes, Γ(L,G) - codes, with L=\α∈ GF(2^2l):G(α)≠ 0 \ and special Goppa polynomials G(x) can be presented as a chain of embedded codes. The true minimal distance has been obtained for all codes of the chain.

Cited by

• A Criterion to Determine True Minimum Distances of Goppa Codes
• Minimum Distances of Binary Goppa Codes and Constructions with Prescribed Alternating Automorphism Groups

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