PERFECT CODES ON SOME ORDERED SETS

Perfect Codes on Some Ordered Sets

Using the concept of codes on ordered sets introduced by Brualdi, Graves and Lawrence, we consider perfect codes on the ordinal sum of two ordered sets, the standard ordered sets and the disjoint sum of two chains. In the classical coding theory all perfect codes are completely described in terms of parameters (cf. [2, 3]). They are mathematically interesting structures. Brualdi et al. [1] rece...

On Some Properties of Symmetrical Perfect Sets

1. Sets of multiplicity of trigonometrical series. We shall consider, throughout the paper, symmetrical perfect sets, that is, sets which are obtained, in the closed interval (0, 2w) by the following process. We divide the interval in three parts of lengths proportional to £1, 1 —2^i, £i, and we remove the central open interval. In the second operation we divide each one of the two intervals le...

On binary 1-perfect additive codes: Some structural properties

The rank and kernel of 1-perfect additive codes is determined. Additive codes could be seen as translation-invariant propelinear codes and, in this correspondence, a characterization of propelinear codes as codes having a regular subgroup of the full group of isometries of the code is established. A characterization of the automorphism group of a 1-perfect additive code is given and also the ca...

Tripled partially ordered sets

In this paper, we introduce tripled partially ordered sets and monotone functions on tripled partiallyordered sets. Some basic properties on these new dened sets are studied and some examples forclarifying are given.

Some Representation Theorems for Partially Ordered Sets