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Examines the classification of optimal linear codes over a finite field up to length 18. Definition of a quaternary linear codes C; Classification of codes up to length 18; Reason for the difficulty of classifying the optimal codes.

Lengths 22 and 30 are so far the only open cases in the classification of extremal formally self-dual even codes. In this paper, a classification of the extremal formally self-dual even codes of length 22 is given. There are 41520 such codes.A variety of properties of these codes are investigated. In particular, new 2-(22, 6, 5) designs are constructed from the codes. [ABSTRACT FROM AUTHOR]

In this paper, twenty new codes of dimension 6 are presented which give improved bounds on the maximum possible minimum distance of quaternary linear codes. These codes belong to the class of quasi-twisted (QT) codes, and have been constructed using a stochastic optimization algorithm, tabu search. A table of upper and lower bounds for d4( n,6) is presented for n≤ 200. [ABSTRACT FROM AUTHOR]

The minimum number of codewords in a binary code with length n and covering radius R is denoted by K(n, R), and corresponding codes are called optimal. A code with M words is said to be balanced in a given coordinate if the number of O's and 1's in this coordinate are at least [M/2]. A code is balanced if it is balanced in all coordinates. It has been conjectured that among optimal covering codes with given parameters there is at least one balanced code. By using a computational method for classifying covering codes, it is shown that there is no balanced code attaining K(9, 1) = 62. [ABSTRACT FROM AUTHOR]