Non-binary block inseparable errors control codes

Abstract

The results of development and research of non-binary block inseparable codes such as mBnq (m > n, q > 2), combining error detection and correction with increase of an information rate are given. The code words are represented by points (vectors) in n-dimensional discrete space with the Minkowski metric (modular metric), appropriate to unsymmetrical multilevel channels. The estimation of the lower and upper bounds of correcting mBnq codes are given. The algorithm of quasi-compact packing of the code words with a given code distance in n-dimensional q-ary space with the Minkowski metric is offered. The block synchronization method on unallowed combinations of q-ary digits appearing on borders of the code words is considered. This method does not reduce an information rate. The estimation of probability of an error in Gaussian channels at usage of 5-ary and 7-ary correcting codes is given. The connection between Hadamard codes and mBnq codes is fixed.