In a distributed storage environment the data file is not placed in just one but in more than one devices which are connected through a network. There are many examples such as RAID systems and Internet storage applications. When data needs to be stored, there is usually one issue it needs to be faced: the availability of such data. Basically, this data needs to be persistent over time and resi...

In this paper we present a description of quasi-cyclic codes which relies on matrices and gives an efficient algorithm for their construction.

Unit memory convolutional codes with generator matrices, which are composed of circulant suhmatrices, are introduced. This structure facilitates the analysis as well as an efficient search for good codes. Equivalences among such codes and consider some of the basic structural properties are discussed. In particular, catastrophic encoders and minimal encoders are characterized and dual codes tre...

In this paper a class of linear error-correcting block codes is investigated. These quasicyclic codes are closely related in structure to cyclic codes although they are not nearly as well understood. I t is shown that an important subclass of the class of cyclic codes is almost equivMent to quasicyclic codes. Also, a short computer generated list of the best quasicyclic codes of rate 1⁄2 is giv...

Given a finite associative ring with unity, R, any free (left) cyclic submodule (FCS) generated by a unimodular (n + 1)-tuple of elements of R represents a point of the n-dimensional projective space over R. Suppose that R also features FCSs generated by (n+1)-tuples that are not unimodular: what kind of geometry can be ascribed to such FCSs? Here, we (partially) answer this question for n = 2 ...

Let $R$ be an arbitrary ring and $T$ be a submodule of an $R$-module $M$. A submodule $N$ of $M$ is called $T$-small in $M$ provided for each submodule $X$ of $M$, $Tsubseteq X+N$ implies that $Tsubseteq X$. We study this mentioned notion which is a generalization of the small submodules and we obtain some related results.

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...

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...