{"title":"A class of triple-twisted GRS codes","authors":"Kapish Chand Meena, Piyush Pachauri, Ambrish Awasthi, Maheshanand Bhaintwal","doi":"10.1007/s10623-025-01595-y","DOIUrl":null,"url":null,"abstract":"<p>This paper focuses on the study of triple-twisted generalized Reed–Solomon (TTGRS) codes over a finite field <span>\\({\\mathbb {F}}_q\\)</span>, having twists <span>\\(\\varvec{t} = (1, 2, 3)\\)</span> and hooks <span>\\(\\varvec{h} = (0, 1, 2)\\)</span>. We have obtained the necessary and sufficient conditions for such TTGRS codes to be MDS, AMDS, and AAMDS via algebraic techniques. We have also enumerated these codes for some particular values of the parameters. Moreover, we have presented some non-trivial examples for MDS, AMDS, and AAMDS TTGRS codes with various parameters. Further, we have studied the hulls of these codes, and under various conditions, obtained necessary and sufficient conditions for these codes to have a hull with dimensions varying from 0 to 5.</p>","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"194 1","pages":""},"PeriodicalIF":1.4000,"publicationDate":"2025-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Designs, Codes and Cryptography","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s10623-025-01595-y","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"COMPUTER SCIENCE, THEORY & METHODS","Score":null,"Total":0}
引用次数: 0
Abstract
This paper focuses on the study of triple-twisted generalized Reed–Solomon (TTGRS) codes over a finite field \({\mathbb {F}}_q\), having twists \(\varvec{t} = (1, 2, 3)\) and hooks \(\varvec{h} = (0, 1, 2)\). We have obtained the necessary and sufficient conditions for such TTGRS codes to be MDS, AMDS, and AAMDS via algebraic techniques. We have also enumerated these codes for some particular values of the parameters. Moreover, we have presented some non-trivial examples for MDS, AMDS, and AAMDS TTGRS codes with various parameters. Further, we have studied the hulls of these codes, and under various conditions, obtained necessary and sufficient conditions for these codes to have a hull with dimensions varying from 0 to 5.
期刊介绍：
Designs, Codes and Cryptography is an archival peer-reviewed technical journal publishing original research papers in the designated areas. There is a great deal of activity in design theory, coding theory and cryptography, including a substantial amount of research which brings together more than one of the subjects. While many journals exist for each of the individual areas, few encourage the interaction of the disciplines.
The journal was founded to meet the needs of mathematicians, engineers and computer scientists working in these areas, whose interests extend beyond the bounds of any one of the individual disciplines. The journal provides a forum for high quality research in its three areas, with papers touching more than one of the areas especially welcome.
The journal also considers high quality submissions in the closely related areas of finite fields and finite geometries, which provide important tools for both the construction and the actual application of designs, codes and cryptographic systems. In particular, it includes (mostly theoretical) papers on computational aspects of finite fields. It also considers topics in sequence design, which frequently admit equivalent formulations in the journal’s main areas.
Designs, Codes and Cryptography is mathematically oriented, emphasizing the algebraic and geometric aspects of the areas it covers. The journal considers high quality papers of both a theoretical and a practical nature, provided they contain a substantial amount of mathematics.
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