Additive codes with few weights

Panario D., ŞAHİN M., Wang Q.

Cryptography and Communications, vol.16, no.5, pp.1077-1102, 2024 (SCI-Expanded, Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 16 Issue: 5
  • Publication Date: 2024
  • Doi Number: 10.1007/s12095-024-00720-3
  • Journal Name: Cryptography and Communications
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Compendex, INSPEC, zbMATH
  • Page Numbers: pp.1077-1102
  • Keywords: 11T71, 94B05, Additive codes, Fq-linear codes, Weight distribution, Weil-like sums
  • Ankara University Affiliated: Yes

Abstract

Additive codes have a wide range of applications. A classical nice and generic way to construct linear codes is via trace functions. In this paper, first, we generalize this method to construct additive codes. Then, we use this method to get some explicit additive codes. Computing Weil-like sums, we obtain parameters of these codes such as the length and weight distribution. We show that our codes have few weights.