We consider linear cyclic codes with the locality property, or locally recoverable codes (LRC codes). A family of LRC codes that generalize the classical construction of Reed-Solomon codes was constructed in a recent paper by I. Tamo and A. Barg (IEEE Trans. Inform. Theory, no. 8, 2014). In this paper we focus on optimal cyclic codes that arise from this construction. We give a characterization...

Abstract. The problem of identifying whether the family of cyclic codes is asymptotically good or not is a long-standing open problem in the field of coding theory. It is known in the literature that some families of cyclic codes such as BCH codes and Reed-Solomon codes are asymptotically bad, however in general the answer to this question is not known. A recent result by Nelson and Van Zwam sh...

ABSTRACT In this paper, we show the equivalence of Space-Time block coding to multipath propagation with respect to Cyclic Delay Diversity for OFDM systems. Hence, we can apply existing Space-Time code design criteria and analyze methods for Space-Time code construction using Cyclic Delay Diversity OFDM systems in multipath propagation environments. i.e. terms like "diversity gain" and "coding ...

The coset graph of a nondegenerate cyclic code is orbital regular. This yields a lower bound on its average distance, a parameter which measures the average distortion of a code used in data compression. Using results of Shahrokhi and Sz&kely we generalize this bound to binary codes with a transitive automorphism group. @ 1998 Elsevier Scienc B.V. All rights reserved

Let p be a prime number. In this paper, we study cyclic codes over the ring Z p [u, v]/u 2 , v 2 , uv − vu. We find a unique set of generators for these codes. We also study the rank and the Hamming distance of these codes. We obtain all except one ternary optimal code of length 12 as the Gray image of the cyclic codes over the ring Z p [u, v]/u 2 , v 2 , uv − vu. We also characterize the p-ary...

There are many ways to find lower bounds for the minium distance of a cyclic code, based on investigation of the defining set. Some new theorems are derived. These and earlier techniques are applied to find lower bounds for the minimum distance of ternary cyclic codes. Furthermore, the exact minimum distance of ternary cyclic codes of length less than 40 is computed numerically. A table is give...

Let $R=\mathbb{Z}_4+u\mathbb{Z}_4,$ where $\mathbb{Z}_4$ denotes the ring of integers modulo $4$ and $u^2=0$. In the present paper, we introduce a new Gray map from $R^n$ to $\mathbb{Z}_{4}^{2n}.$ We study $(1+2u)$-constacyclic codes over $R$ of odd lengths with the help of cyclic codes over $R$. It is proved that the Gray image of $(1+2u)$-constacyclic codes of length $n$ over $R$ are cyclic c...

Resumo Maximum Distance Separable (MDS) convolutional codes are characterized through the property that the free distance meets the generalized Singleton bound. The existence of free MDS convolutional codes over Zpr was recently discovered in [26] via the Hensel lift of a cyclic code. In this paper we further investigate this important class of convolutional codes over Zpr from a new perspectiv...

From ds-bounds for cyclic codes to true distance for abelian codes. Abstract In this paper we develop a technique to extend any bound for the minimum distance of cyclic codes constructed from its defining sets (ds-bounds) to abelian (or multivariate) codes through the notion of B-apparent distance. We use this technique to improve the searching for new bounds for the minimum distance of abelian...

For any prime number p, positive integers m, k, n satisfying gcd(p, n) = 1 and λ0 ∈ F × pm, we prove that any λ p 0 -constacyclic code of length p n over the finite field Fpm is monomially equivalent to a matrix-product code of a nested sequence of p λ0-constacyclic codes with length n over Fpm.