Generator polynomials of cyclic expurgated or extended Goppa codes

2024/05/28 by Xue Jia, Jia, Xue, Fengwei Li +5
Computer Science · Medicine · #Cancer Mechanisms and Therapy #Coding theory and cryptography #FOS: Computer and information sciences #Information Theory (cs.IT) #Peptidase Inhibition and Analysis

paper · pdf · doi:10.48550/arxiv.2405.18023

openalex publication_date 2024/05/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Classical Goppa codes are a well-known class of codes with applications in code-based cryptography, which are a special case of alternant codes. Many papers are devoted to the search for Goppa codes with a cyclic extension or with a cyclic parity-check subcode. Let \Bbb F_q be a finite field with q=2^l elements, where l is a positive integer. In this paper, we determine all the generator polynomials of cyclic expurgated or extended Goppa codes under some prescribed permutations induced by the projective general linear automorphism A ∈ PGL₂(\Bbb F_q). Moreover, we provide some examples to support our findings.

Related

• Binary irreducible quasi-cyclic parity-check subcodes of Goppa codes and extended Goppa codes
• The number of extended irreducible binary Goppa codes
• Generator polynomials and generator matrix for quasi cyclic codes
• Enumeration of irreducible and extended irreducible Goppa codes
• Generator matrix for two-dimensional cyclic codes of arbitrary length