Orthogonal sets of vectors over Zm

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Abstract

The theory of Hadamard matrices is concerned with finding maximal sets of orthogonal vectors whose components are +1's and -1's. A natural generalization of this problem is to allow entries other than ±1's or to allow entries from some fixed field or ring. In the case of an arbitrary field or ring there may be "orthogonal" sets of "vectors" whose cardinality exceeds the "dimension" of the space. The purpose of this paper is to obtain an explicit formula for the maximum cardinality of such an orthogonal set when the ring involved is Zm, the integers modulo m.

Original languageEnglish (US)
Pages (from-to)136-143
Number of pages8
JournalJournal of Combinatorial Theory
Volume9
Issue number2
DOIs
StatePublished - Sep 1970

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