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Designs, Codes and Cryptography

Erschienen in:

16.05.2023

Several families of irreducible constacyclic and cyclic codes

verfasst von: Zhonghua Sun, Xiaoqiang Wang, Cunsheng Ding

Erschienen in: Designs, Codes and Cryptography | Ausgabe 9/2023

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In this paper, several families of irreducible constacyclic codes over finite fields and their duals are studied. The weight distributions of these irreducible constacyclic codes and the parameters of their duals are settled. Several families of irreducible constacyclic codes with a few weights and several families of optimal constacyclic codes are constructed. As by-products, a family of \([2n, (n-1)/2, d \ge 2(\sqrt{n}+1)]\) irreducible cyclic codes over \({\textrm{GF}}(q)\) and a family of \([(q-1)n, (n-1)/2, d \ge (q-1)(\sqrt{n}+1)]\) irreducible cyclic codes over \({\textrm{GF}}(q)\) are presented, where n is a prime such that \({\textrm{ord}}_{2n}(q)=(n-1)/2\) and \({\textrm{ord}}_{(q-1)n}(q)=(n-1)/2\), respectively. The results in this paper complement earlier works on irreducible constacyclic and cyclic codes over finite fields.

Vorheriger Artikel Characterizing subgroup perfect codes by 2-subgroups

Nächster Artikel Meet-in-the-middle attack with splice-and-cut technique and a general automatic framework

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Titel: Several families of irreducible constacyclic and cyclic codes
verfasst von: Zhonghua Sun
Xiaoqiang Wang
Cunsheng Ding
Publikationsdatum: 16.05.2023
Verlag: Springer US
Erschienen in: Designs, Codes and Cryptography / Ausgabe 9/2023
Print ISSN: 0925-1022
Elektronische ISSN: 1573-7586
DOI: https://doi.org/10.1007/s10623-023-01242-4

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Several families of irreducible constacyclic and cyclic codes

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