Cyclotomic constructions of skew Hadamard difference sets

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:119

Article

Feng, Tao¹  Xiang, Qing¹ 

[1] Univ Delaware, Dept Math Sci, Newark, DE 19716 USA

关键词: Cyclotomy;    Difference set;    Gauss sum;    Index 2 Gauss sum;    Partial difference set;    Skew Hadamard difference set;   

DOI  :  10.1016/j.jcta.2011.08.007

来源: Elsevier

【 摘 要 】

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 by using union of cyclotomic classes of F-q of order N = 2p(1)(m), where p(1) is a prime and in a positive integer. Our main tools are index 2 Gauss sums, instead of cyclotomic numbers. (C) 2011 Elsevier Inc. All rights reserved.

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