Algebraic structure of codes over Fq , closed under arbitrary abelian group G of permutations with exponent relatively prime to q, called G-invariant codes, is investigated using a transform domain approach. In particular, this general approach unveils algebraic structure of quasicyclic codes, abelian codes, cyclic codes, and quasi-abelian codes with restriction on G to appropriate special case...

In this work we investigate the weight structure of cyclic codes of composite length n = n l n 2 , where n1 and n2 are relatively prime. The actual minimum distances of some classes of binary cyclic codes of composite length are derived. For other classes new lower bounds on the minimum distance are obtained. These new lower bounds improve on the BCH bound for a considerable number of binary cy...

In this article, we study the skew cyclic codes over R_{k}=F_{p}+uF_{p}+\dots +u^{k-1}F_{p} of length n. We characterize the skew cyclic codes of length $n$ over R_{k} as free left R_{k}[x;\theta]-submodules of R_{k}[x;\theta]/\langle x^{n}-1\rangle and construct their generators and minimal generating sets. Also, an algorithm has been provided to encode and decode these skew cyclic codes.

In this paper we introduce self-dual cyclic and quantum codes over Zα2 × (Z2 + uZ2) . We determine the conditions for any Z2Z2[u]-cyclic code to be self-dual, that is, C = C. Since the binary image of a selforthogonal Z2Z2[u]-linear code is also a self-orthogonal binary linear code, we introduce quantum codes over Zα2 × (Z2 + uZ2) β . Finally, we present some examples of self-dual cyclic and qu...

We study covering codes of permutations with the l∞-metric. We provide a general code construction, which uses smaller building-block codes. We study cyclic transitive groups as building blocks, determining their exact covering radius, and showing linear-time algorithms for finding a covering codeword. We also bound the covering radius of relabeled cyclic transitive groups under conjugation. In...

Cyclic codes have attracted a lot of research interest for decades. In this paper, for an odd prime p, we propose a general strategy to compute the complete weight enumerator of cyclic codes via the value distribution of the corresponding exponential sums. As applications of this general strategy, we determine the complete weight enumerator of several p-ary cyclic codes and give some examples t...

Let R be a finite commutative chain ring with unique maximal ideal 〈γ〉, and let n be a positive integer coprime with the characteristic of R/〈γ〉. In this paper, the algebraic structure of cyclic codes of length n over R is investigated. Some new necessary and sufficient conditions for the existence of nontrivial self-dual cyclic codes are provided. An enumeration formula for the self-dual cycli...

The cyclic codes with parity check polynomial the reciprocal of the characteristic polynomial of the Fibonacci recurrence over a prime finite field are shown to have either one weight or two weights. When these codes are irreducible cyclic we obtain many counterexamples to the conjectural classification of two-weight irreducible cyclic codes of Schmidt and White (2002). When they are reducible ...

We give the class of finite groups which arise as the permutation groups of cyclic codes over finite fields. Furthermore, we extend the results of Brand and Huffman et al. and we find the properties of the set of permutations by which two cyclic codes of length p can be equivalent. We also find the set of permutations by which two quasi-cyclic codes can be equivalent.