Constructions of self-orthogonal codes and LCD codes from functions over finite fields

Sihem Mesnager; Ahmet SINAK

Paper 2024/1860

Constructions of self-orthogonal codes and LCD codes from functions over finite fields

Sihem Mesnager

, Paris 8 University

Ahmet SINAK

, Akdeniz University

Abstract

The construction of self-orthogonal codes from functions over finite fields has been widely studied in the literature. In this paper, we construct new families of self-orthogonal linear codes with few weights from trace functions and weakly regular plateaued functions over the finite fields of odd characteristics. We determine all parameters of the constructed self-orthogonal codes and their dual codes. Moreover, we employ the constructed $p$-ary self-orthogonal codes to construct $p$-ary LCD codes.

Metadata

Available format(s): PDF
Category: Foundations
Publication info: Preprint.
Keywords: Linear code Self-orthogonal code LCD code Weakly regular plateaued function
Contact author(s): smesnager @ univ-paris8 fr
ahmetsinak @ akdeniz edu tr
History: 2024-11-15: revised; 2024-11-14: received; See all versions
Short URL: https://ia.cr/2024/1860
License: CC BY

BibTeX

@misc{cryptoeprint:2024/1860,
      author = {Sihem Mesnager and Ahmet SINAK},
      title = {Constructions of self-orthogonal codes and {LCD} codes from functions over finite fields},
      howpublished = {Cryptology {ePrint} Archive, Paper 2024/1860},
      year = {2024},
      url = {https://eprint.iacr.org/2024/1860}
}