Perfect Difference Set

A set of residues {a_1,a_2,...,a_(k+1)} (mod n) such that every nonzero residue can be uniquely expressed in the form a_i-a_j. Examples include {1,2,4} (mod 7) and {1,2,5,7} (mod 13). A necessary condition for a difference set to exist is that n be of the form k^2+k+1. A sufficient condition is that k be a prime power. Perfect sets can be used in the construction of perfect rulers.

See also

Perfect Ruler

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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.

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Perfect Difference Set

Cite this as:

Weisstein, Eric W. "Perfect Difference Set." From MathWorld--A Wolfram Web Resource.

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