Optimal GQPC Codes over the Finite Field F q

Kundan Suxena, Om Prakash (), Indibar Debnath and Patrick Solé ()
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Kundan Suxena: Department of Mathematics, Indian Institute of Technology Patna, Patna 801106, India
Om Prakash: Department of Mathematics, Indian Institute of Technology Patna, Patna 801106, India
Indibar Debnath: Department of Mathematics, Indian Institute of Technology Patna, Patna 801106, India
Patrick Solé: I2M Lab, CNRS, Aix-Marseille University, Centrale Marseille, 13009 Marseille, France

Mathematics, 2025, vol. 13, issue 22, 1-20

Abstract: This paper presents the algebraic structure of generalized quasi-polycyclic (GQPC) codes, which is a generalization of the right quasi-polycyclic (QPC) and generalized quasi-cyclic (GQC) codes over a finite field F q . Here, we mainly study the multi-generator polynomial of the right GQPC codes of index l . In this regard, we use the Chinese Remainder Theorem to decompose the right GQPC codes into their constituent codes. Further, we determine the dimension of a right GQPC code and provide a method for finding a normalized generating set for a multi-generator right GQPC code. As a by-product, we provide some examples of GQPC codes and obtain several optimal and near-optimal 2-generator right GQPC codes of index 2 over F 2 .

Keywords: right polycyclic codes; quasi-polycyclic codes; normalized generating set of polynomials; optimal codes (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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