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Some results on skew Hadamard difference sets

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Abstract

In this paper, we present two constructions of divisible difference sets based on skew Hadamard difference sets. A special class of Hadamard difference sets, which can be derived from a skew Hadamard difference set and a Paley type regular partial difference set respectively in two groups of orders v 1 and v 2 with |v 1 − v 2| = 2, is contained in these constructions. Some result on inequivalence of skew Hadamard difference sets is also given in the paper. As a consequence of Delsarte’s theorem, the dual set of skew Hadamard difference set is also a skew Hadamard difference set in an abelian group. We show that there are seven pairwisely inequivalent skew Hadamard difference sets in the elementary abelian group of order 35 or 37, and also at least four pairwisely inequivalent skew Hadamard difference sets in the elementary abelian group of order 39. Furthermore, the skew Hadamard difference sets deduced by Ree-Tits slice symplectic spreads are the dual sets of each other when q ≤ 311.

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  1. State Key Laboratory of Information Security, Graduate School of Chinese Academy of Sciences, Beijing, 100049, People’s Republic of China

    Guobiao Weng & Lei Hu

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  1. Guobiao Weng
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  2. Lei Hu
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Correspondence to Guobiao Weng.

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Communicated by Q. Xiang.

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Weng, G., Hu, L. Some results on skew Hadamard difference sets. Des. Codes Cryptogr. 50, 93–105 (2009). https://doi.org/10.1007/s10623-008-9216-4

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  • DOI: https://doi.org/10.1007/s10623-008-9216-4

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