Symmetry groups of Rosenbloom-Tsfasman spaces

Let F(q)(m.n) he the vector space of m . n-tuples over a finite field Fit and P = {1, 2,..., m - n} a poset that is the finite union of In disjoint chains of length it. We consider on F(q)(m.n) the poset-metric d(p) introduced by Rosenbloom and Tsfasman. In this paper, we give a complete description of the symmetry group of the metric space (V, d(p)). (C) 2008 Elsevier B.V. All rights reserved.Let F(q)(m.n) he the vector space of m . n-tuples over a finite field Fit and P = {1, 2,..., m - n} a poset that is the finite union of In disjoint chains of length it. We consider on F(q)(m.n) the poset-metric d(p) introduced by Rosenbloom and Tsfasman.3094763771FAPESP - FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULOsem informaçãoThe authors would like to thank the anonymous referee for valuable remarks which led to sensible improvements in the text and in the proof

Error-block codes and poset metrics

Let P = ({1, 2,..., n}, <=) be a poset, let V-1, V-2,...,V-n, be a family of finite-dimensional spaces over a finite field F-q and let V = V-1 circle plus V-2 circle plus ... V-n. In this paper we endow V with a poset metric such that the P-weight is constant on the non-null vectors of a component V-i, extending both the poset metric introduced by Brualdi et al. and the metric for linear error-block codes introduced by Feng et al.. We classify all poset block structures which admit the extended binary Hamming code [8; 4; 4] to be a one-perfect poset block code, and present poset block structures that turn other extended Hamming codes and the extended Golay code [24; 12; 8] into perfect codes. We also give a complete description of the groups of linear isometrics of these metric spaces in terms of a semi-direct product, which turns out to be similar to the case of poset metric spaces. In particular, we obtain the group of linear isometrics of the error-block metric spaces.Let P = ({1, 2,..., n}, <=) be a poset, let V-1, V-2,...,V-n, be a family of finite-dimensional spaces over a finite field F-q and let V = V-1 circle plus V-2 circle plus ... V-n. In this paper we endow V with a poset metric such that the P-weight is cons2195111FAPESP - FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULOsem informaçã

Bounds for complexity of syndrome decoding for poset metrics

In this work we show how to decompose a linear code relatively to any given poset metric. We prove that the complexity of syndrome decoding is determined by a maximal (primary) such decomposition and then show that a refinement of a partial order leads to a refinement of the primary decomposition. Using this and considering already known results about hierarchical posets, we can establish upper and lower bounds for the complexity of syndrome decoding relatively to a poset metric.Comment: Submitted to ITW 201

Self-dual codes in the Rosenbloom-Tsfasman metric

This paper deals with the study and construction of self-dual codes equipped with the Rosenbloom-Tsfasman metric (RT-metric, in short). An [s, k] linear code in the RT-metric over Fq has codewords with k different non-zero weights. Using the generator matrix in standard form of a code in the RT-metric, the standard information set for the code is defined. Given the standard information set for a code, that for its dual is obtained. Moreover, using the basic parameters of a linear code, the covering radius and the minimum distance of its dual are also obtained. Eventually, necessary and sufficient conditions for a code to be self-dual are established. In addition, some methods for constructing self dual codes are proposed and illustrated with examples