Work

Generator Polynomials of Cyclic Expurgated or Extended Goppa Codes

Year: 2024

Type: article

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$A \in PGL_{2}(\Bbb F_{q})$. Moreover, we provide some examples to support our findings.

Source: IEEE Transactions on Information Theory

DOI: 10.1109/tit.2024.3462712

Authors: Xue Jia, Fengwei Li, Huan Sun, Qin Yue

Institutions: Nanjing University of Aeronautics and Astronautics, Nanjing University of Posts and Telecommunications

Language: English

Topic: Coding theory and cryptography

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: green