Balancing Sets of Vectors

N. Alon, E. E. Bergmann, D. Coppersmith, A. M. Odlyzko

Research output: Contribution to journalArticlepeer-review

62 Scopus citations


For n > 0, d≥ 0, n = d (mod2), let K(n,d) denote the minimal cardinality of a family V of ± 1 vectors of dimension n, such that for any + 1 vector w of dimension n there is a viv such that v·w ≤ d, where v · w is the usual scalar product of v and w. A generalization of a simple construction due to Knuth shows that K(n, d)≤[n/(d + 1)]. A linear algebra proof is given here that this construction is optimal, so that K(n,d) = [n/(d +1)] for all n = d (mod2). This construction and its extensions have applications to communication theory, especially to the construction of signal sets for optical data links.

Original languageEnglish (US)
Pages (from-to)128-130
Number of pages3
JournalIEEE Transactions on Information Theory
Issue number1
StatePublished - Jan 1988
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences


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