Perfect Difference Set -- from Wolfram MathWorld

Perfect Difference Set

A set of residues ${a_1,a_2,...,a_(k+1)}$ (mod ) such that every nonzero residue can be uniquely expressed in the form . Examples include (mod 7) and (mod 13). A necessary condition for a difference set to exist is that be of the form . A sufficient condition is that be a prime power. Perfect sets can be used in the construction of perfect rulers.

REFERENCES:

Guy, R. K. "Modular Difference Sets and Error Correcting Codes." §C10 in Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, pp. 118-121, 1994.

CITE THIS AS:

Weisstein, Eric W. "Perfect Difference Set." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/PerfectDifferenceSet.html