We present a new class of MDS array codes of size n n (n a prime number) called X-Code. The X-Codes are of minimum column distance 3, namely, they can correct either one column error or two column erasures. The key novelty in X-code is that it has a simple geometrical construction which achieves encoding/update optimal complexity, namely, a change of any single information bit a ects exactly tw...

Proper data placement schemes based on erasure correcting code are one of the most important components for a highly available data storage system. A new class of Maximum Distance Separable (MDS) array codes is presented for correcting triple storage failures, which is an extension of the double-erasure-correcting EVENODD code and is called the HDD-EOD code. The encoding and decoding procedures...

Given a regular multiset [Formula: see text] on text], partial order and label map defined by with we define pomset block metric the direct sum of based text]. The extends classical introduced Sudha Selvaraj generalizes poset Alves et al. over space is called determine complete weight distribution it. Further, text]-perfect codes for ideals full counts are described. Then, chain pomset, packing...

Given an (n, k) linear code C over GF(q), the intersection of C with a code ?(C), where ? # Sn , is an (n, k1) code, where max[0, 2k&n] k1 k. The intersection problem is to determine which integers in this range are attainable for a given code C. We show that, depending on the structure of the generator matrix of the code, some of the values in this range are attainable. As a consequence we giv...

In this paper, we study the linear codes over the commutative ring R = Z4 + vZ4, where v2 = v. We define the Gray weight of the elements of R and give a Gray map from Rn to Z2n 4 , which lead to the MacWillams identity of the linear code over R. Some useful results on self-dual code over R are given. Furthermore, the relationship between some complex unimodular lattices and Hermitian self-dual ...

Broadcast of a message to nodes in a network is one of elementary but inevitable techniques in wireless ad-hoc and sensor networks. In this paper, we apply the protocol, which the authors proposed for cooperative multi-hop relay networks, to message broadcast over random error channels. Performance is evaluated in terms of the delivery ratio by means of computer simulations. The proposed protoc...

Traditionally, communication networks are composed of routing nodes, which relay and duplicate data. Work in recent years has shown that for the case of multicast, an improvement in both rate and code-construction complexity can be gained by replacing these routing nodes by linear coding nodes. These nodes transmit linear combinations of the inputs transmitted to them. In this work, we deal wit...

As a specialization of model-driven architecture, model-driven security (MDS) is an approach that uses models to capture and represent a system’s architecture and security requirements in software development. Through layers of abstraction, system designers and developers can leverage simple and abstract models to design large and complex systems and generate system artifacts such as security p...

In this paper, we first introduce the concept of elementary linear subspace, which has similar properties to those of a set of coordinates. We then use elementary linear subspaces to derive properties of maximum rank distance (MRD) codes that parallel those of maximum distance separable (MDS) codes. Using these properties, we show that, for MRD codes with error correction capability t, the deco...

From the generating matrix of a linear code one can construct a sequence of generalized star configurations which are strongly connected to the generalized Hamming weights and the underlying matroid of the code. When the code is MDS, the matrix is generic and we obtain the usual star configurations. In our main result, we show that the degree of a generalized star configuration as a projective ...