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Some New Difference Sets

Published online by Cambridge University Press:  20 November 2018

Basil Gordon ,
W. H. Mills  and
L. R. Welch
Basil Gordon
Affiliation:
University of California
W. H. Mills
Affiliation:
Yale University
L. R. Welch
Affiliation:
Institute for Defense Analyses, Princeton
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A difference set is a set D = {d1, d2, … , dk] of k distinct residues modulo v such that each non-zero residue occurs the same number of times among the k(k — 1) differences di — dj, i ≠ j. If λ is the number of times each difference occurs, then

(1)

When we wish to emphasize the particular values of v, k, and λ involved we will call such a set a (v, k, λ) difference set. Another (v, k, λ) difference set E = {e1, e2, … ek} is said to be equivalent to the original one if there exist a and t such that (t, v) = 1 and E = {a + td1, … , a + tdk}. If t = 1 we will call the set E a slide of the set D. If D = E, then t is called a multiplier of D.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 14 , 1962 , pp. 614 - 625
Copyright
Copyright © Canadian Mathematical Society 1962

References

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