On the generators of F2F4-skew cyclic codes

Sarı M., Aydoğdu İ.

2^nd International Symposium on current developments in fundamental and applied mathematics sciences, Ankara, Turkey, 14 - 17 November 2023, pp.55, (Summary Text)

  • Publication Type: Conference Paper / Summary Text
  • City: Ankara
  • Country: Turkey
  • Page Numbers: pp.55
  • Yıldız Technical University Affiliated: Yes

Abstract

Skew cyclic codes are one of the important family of codes in coding theory which are actually generalization of classical cyclic codes. In this work, we introduce and study the algebraic structure of skew cyclic codes over the mixed alphabet F_2^r * F_4^r where F_2 and F_4 are finite fields of  2 and 4 elements, respectively with non-negative integers r and s. We first determine the generator polynomials of F_2F_4-skew cyclic codes. Further, we relate skew cyclic codes over  F_2F_4 to binary linear codes by defining a linear Gray map. We also investigate the duals of skew cyclic codes over this mixed alphabet. We show that the dual of any F_2F_4-skew cyclic code is another F_2F_4-skew cyclic code. As an application of our work, we provide several examples of F_2F_4-skew cyclic codes whose binary images have optimal parameters under the Gray mapping. We also consider the quantum codes over F_2^r * F_4^r. By using the well-known construction method of quantum codes (CSS), we obtain examples of quantum codes with good parameters.

Keywords: Skew cyclic codes, F_2F_4, optimal codes, generator polynomials.