ON GRAY IMAGES OF CONSTACYCLIC CODES OVER THE FINITE RING F-2 + u(1)F(2) + u(2)F(2)

ÖZKAN M., Dertli A., ÇENGELLENMİŞ Y.

TWMS JOURNAL OF APPLIED AND ENGINEERING MATHEMATICS, vol.9, no.4, pp.876-881, 2019 (ESCI) identifier

  • Publication Type: Article / Article
  • Volume: 9 Issue: 4
  • Publication Date: 2019
  • Journal Name: TWMS JOURNAL OF APPLIED AND ENGINEERING MATHEMATICS
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.876-881
  • Keywords: Constacylic code, Gray image, CYCLIC CODES
  • Ondokuz Mayıs University Affiliated: Yes

Abstract

We introduce the finite ring F-2 + u(1)F(2) + u(2)F(2), u(1)(2) = u(1), u(2)(2) = 0, u(1).u(2) = u(2).u(1) = 0 which is not a finite chain ring. We focus on (1 + u(2)) -constacyclic codes over F-2 + u(1)F(2) + u(2)F(2) of odd length. We prove that the Gray image of a linear (1 + u(2)) -constacyclic code over F-2 + u(1)F(2) + u(2)F(2) of odd length n is a quasi-cyclic code of index 4 and length 4 n over F-2.