Constacyclic codes over F_q + u F_q + v F_q + u v F_q

Abstract

Let q be a prime power and F q be a finite field. In this paper, we study constacyclic codes over the ring F q + uF q + vF q + uvF q , where u 2 = u, v 2 = v and uv = vu. We characterize the generator polynomials of constacyclic codes and their duals using some decomposition of this ring. Finally we study the images of self-dual cyclic codes over F 2 m + uF 2 m + vF 2 m + uvF 2 m through a linear Gray map.

Skew cyclic and skew $(α_1 + uα_2 + vα_3 + uvα_4)$-constacyclic codes over $F_q + uF_q + vF_q + uvF_q$

“…where a, b, c, d ∈ F q and by [11], a + ub + vc + uvd ∈ R is a unit if and only if a, (a + b), (a + c), (a + b + c + d) are units in F q . Let C be a linear code of length n in R and…”

“…One of the most important class of linear codes is cyclic code which is easier to implement and also playing crucial role in the development of algebraic coding theory. Latter, cyclic codes over finite rings have got attention of many researchers and hence many new techniques have been discovered to produce cyclic codes over finite commutative ring with better parameters and properties [ [2], [5], [13], [11]]. But all of these works are restricted to the finite commutative rings.…”

Galois LCD Codes Over

“…Li et al [10] studied linear codes over the ring Z 4 + uZ 4 + vZ 4 + uvZ 4 for the Euclidean inner product and discussed some properties of Euclidean dual and MDS codes. Several authors investigated skew cyclic codes, constacyclic codes and quantum error correcting codes over the ring R [1,9,17]. Prakash et al [14] enumerated self-dual and LCD double circulant codes over a class of finite commutative nonchain rings R q and investigated the algebraic structure of 1-generator quasi-cyclic (QC) codes over R q for q = 3.…”