one of the most important problems of coding theory is to construct codes with beat possible minimum distances. In this paper, we use the algebraic structure of quasi-cyclic codes and the BCH type bound on the minimum distance to search for quasi-cyclic codes over IFS, the finite field with five elements, which improve the minimum distances of best-known linear codes. We construct 15 new linear...

We show how to construct quantum stabilizer and subsystem codes from algebro-geometric toric codes extending the known construction of subsystem codes from cyclic codes and extending the construction of stabilizer codes from toric codes in an earlier work by one of the authors. Since algebrogeometric toric codes are higher dimensional extensions of cyclic codes, we obtain this way a new and ric...

In this paper, we investigate the structure of cyclic codes over the ring F3 + vF3 where v2 = 1 and F3 = {0, 1, 2}. We prove that cyclic codes over the ring are principally generated, and give the generator polynomial of cyclic codes over this ring. Mathematics Subject Classification: 94B05

In this paper, we study the theory for constructing DNA cyclic codes of odd length over Z4[u]/〈u 2〉 which play an important role in DNA computing. Cyclic codes of odd length over Z4+uZ4 satisfy the reverse constraint and the reverse-complement constraint are studied in this paper. The structure and existence of such codes are also studied. The paper concludes with some DNA example obtained via ...

We present a family of reducible cyclic codes constructed as the direct sum of two different semiprimitive two-weight irreducible cyclic codes. This family generalizes the class of reducible cyclic codes that was reported in the main result of B. Wang, et al. [11]. Moreover, despite of what was stated therein, we show that, at least for the codes studied here, it is still possible to compute th...

Quasi-cyclic Codes from Cyclic-Structured Designs with Good Properties Dimitris E. Simos and Christos Koukouvinos Department of Mathematics National Technical University of Athens Zografou 15773, Athens, Greece {dsimos,ckoukouv}@math.ntua.gr Quasi-cyclic (QC) codes form an important class of linear codes, which contains the well-known class of cyclic codes. A linear code with a complementary du...

A Z2Z4-additive code C ⊆ Z α 2 ×Z 4 is called cyclic if the set of coordinates can be partitioned into two subsets, the set of Z2 and the set of Z4 coordinates, such that any cyclic shift of the coordinates of both subsets leaves the code invariant. We study the binary images of Z2Z4-additive cyclic codes. We determine all Z2Z4-additive cyclic codes with odd β whose Gray images are linear binar...

In this paper, we study skew cyclic codes over the ring R = Fq + uFq + vFq + uvFq, where u 2 = u, v2 = v, uv = vu, q = p and p is an odd prime. We investigate the structural properties of skew cyclic codes over R through a decomposition theorem. Furthermore, we give a formula for the number of skew cyclic codes of length n over R.

In this paper, it was constructed quantum codes from cyclic codes over finite ring S = F2 + uF2 + vF2, u2 = u, v2 = v, uv = vu = 0 for arbitrary length n. It was given a new Gray map Ψ which is both an isometry and weight preserving map. It was shown that C is self orthogonal codes over S, so is Ψ(C). It was given a necessary and sufficient condition for cyclic codes over S that contains its du...

Let R = F2m +uF2m + · · ·+u k F2m , where F2m is the finite field with 2 m elements, m is a positive integer, and u is an indeterminate with u = 0. In this paper, we propose the constructions of two new families of quantum codes obtained from dual-containing cyclic codes of odd length over R. A new Gray map over R is defined and a sufficient and necessary condition for the existence of dual-con...