In coding theory, a very interesting problem (but at the same time, a very difficult one) is to determine the weight distribution of a given code. This problem is even more interesting for cyclic codes, and this is so, mainly because they possess a rich algebraic structure, which can be utilized in a variety of ways. For example, in Engineering Telecommunications, this structure is commonly emp...

Nowadays acoustic emission (AE) testing based on the Kaiser Effect (KE) is increasingly used to estimate the in-situ stress in laboratories. In this work, this effect is assessed on cylindrical specimens in numerical simulations of the cyclic loadings including loading, unloading, and re-loading cycles using a 3D code called the particle flow code (PFC) based upon the distinct element method. T...

An (n, k) group code over a group G is a subset of G which forms a group under componentwise group operation and can be defined in terms of n — k homomorphisms from G to G. In this correspondence, the set of homomorphisms which define Maximum Distance Separable (MDS) group codes defined over cyclic groups are characterized. Each defining homomorphism can be specified by a set of k endomorpbisms...

The results of J. F. Qian et al. [5] on (1 − γ)-constacyclic codes over finite chain rings of nilpotency index 2 are extended to (1 − γe)constacyclic codes over finite chain rings of arbitrary nilpotency index e+1. The Gray map is introduced for this type of rings. We prove that the Gray image of a linear (1− γe)-constacyclic code over a finite chain ring is a distance-invariant quasi-cyclic co...

We introduce a Gray map from F2m + uF2m to F 2m 2 and study (1 + u)-constacyclic codes over F2m + uF2m ,where u 2 = 0. It is proved that the image of a (1+u)-constacyclic code length n overF2m+uF2m under the Gray map is a distance-invariant quasi-cyclic code of indexm and length 2mn over F2. We also prove that every code of length 2mnwhich is the Gray image of cyclic codes overF2m+uF2m of lengt...

Let Fq be a finite field with q elements, where q = p , p is a prime, and s is a positive integer. An [n, k, d] linear code C is a k-dimensional subspace of Fq with minimum distance d. It is called cyclic if (c0, c1, . . . , cn−1) ∈ C implies (cn−1, c0, c1, . . . , cn−2) ∈ C. By identifying the vector (c0, c1, . . . , cn−1) ∈ Fq with c0 + c1x+ c2x 2 + · · ·+ cn−1c ∈ Fq[x]/(x − 1), any code C of...

This paper develops a constant amortized time algorithm to produce a cyclic cool-lex Gray code for fixed-density binary necklaces, Lyndon words, and pseudo-necklaces. It is the first Gray code for these objects that achieves this time bound. The algorithm is applied: (i) to develop a constant amortized time cyclic Gray code for necklaces, Lyndon words, and pseudo-necklaces ordered by density an...

In the present paper, we study skew cyclic codes over the ring $F_{q}+vF_{q}+v^2F_{q}$, where $v^3=v,~q=p^m$ and $p$ is an odd prime. We investigate the structural properties of skew cyclic codes over $F_{q}+vF_{q}+v^2F_{q}$ using decomposition method. By defining a Gray map from $F_{q}+vF_{q}+v^2F_{q}$ to $F_{q}^3$, it has been proved that the Gray image of a skew cyclic code of length $n$ ove...

As a generalization of cyclic codes, quasi-cyclic codes contain many good linear codes. Extensive search is made and lots of good quasi-cyclic codes are obtained from irreducible cyclic codes. A new binary [95, 13, 40] code which improves the lower bound on the minimum distance, is also constructed. Index Term — Codes and coding, linear codes, cyclic codes, idempotent, irreducible codes, quasi-...

We study cyclic codes of length pk over GR(p2,m), or equivalently, ideals of the ring GR(p2,m)/ 〈upk − 1〉. We derive a method of representing the ideals, and classify all ideals in the ring GR(p2,m)/ 〈upk − 1〉. We also analyse the duals, and identify the self-dual ideals. © 2008 Elsevier Inc. All rights reserved.