Some Combinatorial Problems in Coding and Information Theory

We consider several solved and unsolved problems from the combinatorial coding and information theory such as multiple packing of discrete spaces, bounds for the probability of error in discrete channels. We expose recent progress in solving these problems for large sizes of alphabets. Also we introduce some new in coding and information theory problems which allow us to obtain nal (in some sense) results in this area. I should like to introduce some problems in coding and information theory which I study for several years and this study increase my knowledge of combinatorics of discrete spaces of the set of sequences over nite alphabets. Let's remind some usual notations which we use later. For the arbitrary set N let's N S denote the set of all S element subsets of N ; in other words N S is the complete uniform hypergraph on vertixes N . For convenience we also denote [N ] = N 1 . Let's [M ] denote the set of all sequences of length n with symbols from the alphabet [M ]. We impose to the set [M ] the Hamming metrics d( ; ). For the arbitrary set fa1; a2; : : : ; aL+1g [M ] n we denote by t(a1; a2; : : : ; aL+1) = t the maximal positive integer, such that an arbitrary ball Bn(y; t) in [M ] n of radius t does not contain all L+ 1 points a1; a2; : : : ; aL+1, i.e.