The diametric theorem in Hamming spaces---optimal anticodes (Q1271885)

Denote by \({\mathcal H}(n, \alpha)\) the Hamming space of \(n\)-length codewords over an \(\alpha\)-element alphabet. The distance of two words is the number of different components. If \(\alpha =2\) then the codewords naturally coincide with the subsets of an \(n\)-element set, and distances are closely related to the sizes of intersections. A codeword set in \({\mathcal H}(n, \alpha)\) with prescribed diameter is called anticode. The anticodes can be considered as the duals of codes. This paper determines the maximum cardinality of anticodes. The result is based on the seminal result of the authors: The complete intersection theorem for systems of finite sets, Eur. J. Comb. 18, No. 2, 125-136, Art. No. ej950092 (1997; Zbl 0869.05066).