Optimal GQPC Codes over the Finite Field Fq
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 Fq. 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 F2.
Authors
- Indibar Debnath (ORCID: https://orcid.org/0009-0003-2511-5066)
- Patrick Solé (ORCID: https://orcid.org/0000-0002-4078-8301)
- Om Prakash (ORCID: https://orcid.org/0000-0002-6512-4229)
- Kundan Suxena (ORCID: https://orcid.org/0009-0001-0830-4127)
Institutions
- Centre National de la Recherche Scientifique (FR)
- Indian Institute of Technology Patna (IN)
- Centrale Méditerranée (FR)
- Institut Polytechnique de Bordeaux (FR)
Publication Details
- Journal
- Mathematics
- Published
- 2025-11-14
- DOI
- https://doi.org/10.3390/math13223655
- Primary Topic
- Coding theory and cryptography
- Type
- article
- Field-Weighted Citation Impact
- 0.00