A set of residues (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.

# Perfect Difference Set

## See also

Perfect Ruler## Explore with Wolfram|Alpha

## 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.

## Referenced on Wolfram|Alpha

Perfect Difference Set## Cite this as:

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