Cyclotomic Constructions of Skew Hadamard Difference Sets

Details Cyclotomic Constructions of Skew Hadamard Difference Sets Cyclotomic Constructions of Skew Hadamard Difference Sets

2011-01-15

arxiv.org/abs/1101.2994v2

Mathematics

Combinatorics

15 pages; corrected a few typos; to appear in J. Combin. Theory (A)

Scientific paper

We revisit the old idea of constructing difference sets from cyclotomic
classes. Two constructions of skew Hadamard difference sets are given in the
additive groups of finite fields using unions of cyclotomic classes of order
$N=2p_1^m$, where $p_1$ is a prime and $m$ a positive integer. Our main tools
are index 2 Gauss sums, instead of cyclotomic numbers.

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