In this paper, the structure of cyclic codes over m 2 of length k 2 for any natural number k is studied. It is proved that cyclic codes over     1 2 n x x Z R m / ] [ of length n = k 2 are generated by at most m elements. Keywords— Codes, Cyclic codes, Ideals, Principal ideal Ring

Construction of subspace codes with good parameters is one of the most important problems in random network coding. In this paper we present first a generalization of the concept of cyclic subspaces codes and further we show that the usual methods for constructing cyclic subspace codes over finite fields works for m-quasi cyclic codes, namely the subspaces polynomials and Frobenius mappings.

Two skew cyclic codes can be equivalent for the Hamming metric only if they have the same length, and only the zero code is degenerate. The situation is completely different for the rank metric, where lengths of codes correspond to the number of outgoing links from the source when applying the code on a network. We study rank equivalences between skew cyclic codes of different lengths and, with...

Quasi cyclic codes over a finite field are viewed as cyclic codes over a non commutative ring of matrices over a finite field. This point of view permits to generalize some known results about linear recurring sequences and to propose a new construction of some quasi cyclic codes and self dual codes.

In this paper, we construct MDS Euclidean self-dual codes which are extended cyclic duadic codes. And we obtain many new MDS Euclidean self-dual codes. We also construct MDS Hermitian self-dual codes from generalized Reed-Solomon codes and constacyclic codes. And we give some results on Hermitian self-dual codes, which are the extended cyclic duadic codes.

Let R = Z4[u]/〈u〉 = Z4 + uZ4 + . . . + uZ4 (u = 0) where k ∈ Z satisfies k ≥ 2. For any odd positive integer n, it is known that cyclic codes over R of length n are identified with ideals of the ring R[x]/〈x − 1〉. In this paper, an explicit representation for each cyclic code over R of length n is provided and a formula to count the number of codewords in each code is given. Then a formula to c...

Codes over Fqm that form vector spaces over Fq are called Fq-linear codes over Fqm . Among these we consider only cyclic codes and call them Fq-linear cyclic codes (FqLC codes) over Fqm . This class of codes includes as special cases (i) group cyclic codes over elementary abelian groups (q = p, a prime), (ii) subspace subcodes of Reed-Solomon codes and (iii) linear cyclic codes over Fq (m=1). T...

Abstract: Let Rk,m be the ring F2m [u1, u2, · · · , uk]/ ⟨ ui , uiuj − ujui ⟩ . In this paper, cyclic codes of arbitrary length n over the ring R2,m are completely characterized in terms of unique generators and a way for determination of these generators is investigated. A F2m -basis for these codes is also derived from this representation. Moreover, it is proven that there exists a one-to-one...

Cyclic and self-dual codes are important classes of codes in coding theory. Jia, Ling and Xing [5] as well as Kai and Zhu [7] proved that Euclidean self-dual cyclic codes of length n over Fq exist if and only if n is even and q = 2 , where r is any positive integer. For n and q even, there always exists an [n, n 2 ] self-dual cyclic code with generator polynomial x n 2 + 1 called the trivial se...

In this paper, we study cyclic codes over the Galois ring GR(p, s). The main result is the characterization and enumeration of Hermitian self-dual cyclic codes of length pa over GR(p, s). Combining with some known results and the standard Discrete Fourier Transform decomposition, we arrive at the characterization and enumeration of Euclidean self-dual cyclic codes of any length over GR(p, s). S...