No CrossRef data available.
Article contents
A Generalization of Difference Sets
Published online by Cambridge University Press: 20 November 2018
Extract
Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.
A (v, k, λ) difference set D is a set of k distinct residues {a1, a2, … , ak} modulo v such that every residue b ≢ 0 (mod v) can be expressed in exactly λ ways in the form b ≡ ai — aj (mod v). With each difference set we may associate a binary periodic sequence (s1, s2, …) with si = 1 if i (mod v) is in D, and si = 0 otherwise. Since this sequence is periodic of period v, we need only consider one cycle from the sequence. Such cycles we agree to call (binary) difference cycles. Difference cycles (equivalently, difference sets) have been studied intensively (2, 4). They have important applications to digital communications, mainly because they have 2-level autocorrelation. In this paper we shall point out certain other (equivalent) properties of difference cycles which seem susceptible to immediate generalization, but show that these generalizations are vacuous.
- Type
- Research Article
- Information
- Copyright
- Copyright © Canadian Mathematical Society 1967
References
1.
Bose, R. C., On construction of balanced incomplete block designs, Ann. Eugen.,
9 (1939), 353–399.Google Scholar
2.
Golomb,
et al., Digital communications with space applications (Englewood Cliffs, 1965).Google Scholar
3.
Hananai, H., The existence and construction of balanced incomplete block designs, Ann. Math. Statist.,
32 (1961), 361–386.Google Scholar
5.
Titsworth, R., Correlation properties of random-like periodic sequences, Jet Propulsion Laboratory, Progress Report 20-391, October 1959.Google Scholar
You have
Access