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We develop refinements of the Levenshtein bound in q-ary Hamming spaces by taking into account the discrete nature of the distances versus the continuous behavior of certain parameters used by Levenshtein. We investigate the first relevant cases and present new bounds. In particular, we derive generalizations and q-ary analogs of the MacEliece bound. Furthermore, we provide evidence that our approach is as good as the complete linear programming and discuss how faster are our calculations. Finally, we present a table with parameters of codes which, if exist, would attain our bounds. [ABSTRACT FROM AUTHOR]

We investigate binary orthogonal arrays by making use of the fact that all possible distance distributions of the arrays under investigation and of related arrays can be computed. We apply certain relations for reducing the number of feasible distance distributions. In some cases this leads to nonexistence results. In particular, we prove that there exist no binary orthogonal arrays with parameters (strength, length, cardinality) = (4, 10, 6 · 2), (4, 11, 6 · 2), (4, 12, 7 · 2), (5, 11, 6 · 2), (5, 12, 6 · 2), and (5, 13, 7 · 2). [ABSTRACT FROM AUTHOR]

A method for constructing optimal almost equisymbol codes based on difference matrices is proposed. Some of these codes generate previously unknown optimal equidistant codes satisfying the Plotkin bound. As a consequence, they generate new resolvable balanced incomplete block designs. [ABSTRACT FROM AUTHOR]