Perfect Difference Set
المؤلف:
Guy, R. K.
المصدر:
"Modular Difference Sets and Error Correcting Codes." §C10 in Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag,
الجزء والصفحة:
pp. 118-121
3-11-2020
811
Perfect Difference Set
A set of residues ![<span style=]()
{a_1,a_2,...,a_(k+1)}" src="https://mathworld.wolfram.com/images/equations/PerfectDifferenceSet/Inline1.gif" style="height:15px; width:98px" /> (mod 
) such that every nonzero residue can be uniquely expressed in the form 
. Examples include ![<span style=]()
{1,2,4}" src="https://mathworld.wolfram.com/images/equations/PerfectDifferenceSet/Inline4.gif" style="height:15px; width:47px" /> (mod 7) and ![<span style=]()
{1,2,5,7}" src="https://mathworld.wolfram.com/images/equations/PerfectDifferenceSet/Inline5.gif" style="height:15px; width:62px" /> (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.
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