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, 2022 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Publication Date: 2022
  • Doi Number: 10.1007/s00200-021-00538-z
  • Title of Journal : APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING
  • Keywords: F-q2-double cyclic codes, Hermitian inner product, Self-dual cyclic codes, Optimal codes

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.