Codes with a poset metric

Codes Satisfying the Chain Condition with a Poset Weights

In this paper we extend the concept of generalized Wei weights for poset-weight codes and show that all linear codes C satisfy the chain condition if support of C is a subposet totally ordered.

Classification of perfect linear codes with crown poset structure

Brualdi et al. introduced the concept of poset codes. In this paper, we consider the problem of classifying all perfect linear codes when the set of coordinate positions is endowed with crown poset structure. We derive a Ramanujan–Nagell type diophantine equation which is satis ed by parameters of perfect linear P-code. Solving this equation, we characterize parameters of one and two error corr...

Perfect Codes for Uniform Chains Poset Metrics

The class of poset metrics is very large and contains some interesting families of metrics. A family of metrics, based on posets which are formed from disjoint chains which have the same size, is examined. A necessary and sufficient condition, for the existence of perfect single-errorcorrecting codes for such poset metrics, is proved.

Error-block codes and poset metrics

Properties of Codes with the Rank Metric

In this paper, we study properties of rank metric codes in general and maximum rank distance (MRD) codes in particular. For codes with the rank metric, we first establish Gilbert and sphere-packing bounds, and then obtain the asymptotic forms of these two bounds and the Singleton bound. Based on the asymptotic bounds, we observe that asymptotically Gilbert-Varsharmov bound is exceeded by MRD co...