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The most common decision criteria for decoding are maximum likelihood decoding and nearest neighbor decoding. It is well known that maximum likelihood decoding coincides with nearest neighbor decoding with respect to the Hamming metric on the binary symmetric channel. In this paper, we study channels and metrics for which those two criteria do and do not… (More)
In this paper, we prove that a poset-block space admits a MacWilliams-type identity if and only if the poset is hierarchical, and at any level of the poset, all the blocks have the same dimension. When the poset-block admits the MacWilliams-type identity, we explicitly state the relation between the weight enumerators of a code and its dual.
We investigate linear and additive codes in partially ordered Hamming-like spaces that satisfy the extension property, meaning that automorphisms of ideals extend to automorphisms of the poset. The codes are naturally described in terms of translation association schemes that originate from the groups of linear isometries of the space. We address questions… (More)
In this paper, we extend Wei's Duality Theorem, relating the generalized Hamming weight hierarchy of a code to the hierarchy of the dual code, to the scope of codes with poset metrics. As a consequence of this duality theorem, we prove some results concerning discrepancy of codes and chain condition for generalized weights.
Considering a poset metric as a generalization of Hamming's metric, the packing radius of a code is not necessarily a function of the minimal distance. In this work we show, without any restriction on the poset, that the relation between the weight and the packing radius of a vector is equivalent to a generalization of the classical partition problem. We… (More)
Poset metrics form a generalization of the Hamming metric on the space F<sup>n</sup><sub>q</sub>. Orbits of the group of linear isometries of the space give rise to a translation association scheme. The structure of the dual scheme is important in studying duality of linear codes; this study is facilitated if the scheme is self-dual. We study the relation… (More)