F-q2-double cyclic codes with respect to the Hermitian inner product


AYDOĞDU İ., Abualrub T., Samei K.

APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING, vol.35, no.2, pp.151-166, 2024 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 35 Issue: 2
  • Publication Date: 2024
  • Doi Number: 10.1007/s00200-021-00538-z
  • Journal Name: APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Applied Science & Technology Source, Compendex, Computer & Applied Sciences, INSPEC, MathSciNet, zbMATH
  • Page Numbers: pp.151-166
  • Keywords: F-q2-double cyclic codes, Hermitian inner product, Self-dual cyclic codes, Optimal codes
  • Yıldız Technical University Affiliated: Yes

Abstract

In this paper, we introduce F-q2-double cyclic codes of length n = r + s, where F-q2 is the Galois field of q(2) elements, q is a power of a prime integer p and r, s are positive integers. We determine the generator polynomials for any F-q2-double cyclic code. For any F-q2-double cyclic code C, we will define the Euclidean dual code C-perpendicular to based on the Euclidean inner product and the Hermitian dual code C-perpendicular to H based on the Hermitian inner product. We will construct a relationship between C-perpendicular to and C-perpendicular to H and then find the generator polynomials for the Hermitian dual code C-perpendicular to H. As an application of our work, we will present examples of optimal parameter linear codes over the finite field F-4 and also examples of optimal quantum codes that were derived from F-4-double cyclic codes using the Hermitian inner product.