A linear code, when used for error detection on a symmetric channel, is said to be proper if the corresponding undetected error probability increases monotonously in ", the symbol error probability of the channel. Such codes are generally considered to perform well in error detection. A number of well-known classes of linear codes are proper, e.g., the perfect codes, the MDS codes, MacDonald's ...

We give a general method to construct MDS one-dimensional convolutional codes. Our method generalizes previous constructions [5]. Moreover we give a classification of one-dimensional Convolutional Goppa Codes and propose a characterization of MDS codes of this type. Introduction One of the main problems in coding theory is the construction of codes with a large distance, such as so-called MDS c...

Both linear complementary dual (LCD) codes and maximum distance separable (MDS) have good algebraic structures, they interesting practical applications such as communication systems, data storage, quantum codes, so on. So far, most of LCD MDS been constructed by employing generalized Reed-Solomon codes. In this paper we construct some classes new Euclidean Hermitian which are not monomially equ...

In this paper we discuss an upper bound on the free distance for a rate k / n convolutional code with complexity b . Using th i s bound we in t roduce the notion of a MDS convolutional code. We also give an algebraic way of cons t ruc t ing b inary codes of rate 1/2 and large complexity. The obta ined distances compare favorably to the distances found by computer searches and probabilistic meth...

This paper presents a novel coding scheme for distributed storage systems containing nodes with adversarial errors. The key challenge in such systems is the propagation of the erroneous data from a single corrupted node to the rest of the system during node repair process. We present a concatenated coding scheme which is based on two types of codes: maximum rank distance (MRD) code as an outer ...

We investigate the use of maximum distance separable (MDS) codes to cache popular content to reduce the download delay of wireless content delivery. In particular, we consider a cellular system where devices roam in an out of a cell according to a Poisson random process. Popular content is cached in a limited number of the mobile devices using an MDS code and can be downloaded from the mobile d...

We investigate the covering problem in RT spaces induced by the RosenbloomTsfasman metric, extending the classical covering problem in Hamming spaces. Some connections between coverings in RT spaces and coverings in Hamming spaces are derived. Several lower and upper bounds are established for the smallest cardinality of a covering code in an RT space, generalizing results by Carnielli, Chen an...

Ahstrrrct-A class of convolutional codes called cross parity check (CPC) codes, useful for the protection of data stored on magnetic tape, is described and analyzed. CPC codes are first explained geometrically; their construction is described in terms of constraining data written onto a tape in such a way that, when lines of varying slope are drawn across the tape, the bits falling on those lin...

We propose two coded schemes for the distributed computing problem of multiplying a matrix by a set of vectors. The first scheme is based on partitioning the matrix into submatrices and applying maximum distance separable (MDS) codes to each submatrix. For this scheme, we prove that up to a given number of partitions the communication load and the computational delay (not including the encoding...

MDS matrices allow to build optimal linear diffusion layers in block ciphers. However, MDS matrices cannot be sparse and usually have a large description, inducing costly software/hardware implementations. Recursive MDS matrices allow to solve this problem by focusing on MDS matrices that can be computed as a power of a simple companion matrix, thus having a compact description suitable even fo...