A class of cyclic $(v;k_1,k_2,k_3;\lambda)$ difference families with $v \equiv 3 \pmod{4}$ a prime

Dragomir Z. Djokovic; Ilias S. Kotsireas

A class of cyclic $(v;k_1,k_2,k_3;\lambda)$ difference families with $v \equiv 3 \pmod{4}$ a prime

Combinatorics 2017-10-12 v2

Authors: Dragomir Z. Djokovic , Ilias S. Kotsireas

Abstract

We construct several cyclic $(v;k_1,k_2,k_3;\lambda)$ difference families with $v\equiv3 \pmod{4}$ a prime and $\lambda=k_1+k_2+k_3-(3v-1)/4$ . Such families can be used in conjunction with the well-known Paley-Todd difference sets to construct skew-Hadamard matrices of order $4v$ . Our main result is that we have constructed for the first time the example of skew-Hadamard matrices of orders $4\cdot239=956$ and $4\cdot331=1324$ .

Keywords

cyclic difference families skew-Hadamard matrices Paley-Todd difference sets prime order combinatorial designs

Cite

@article{arxiv.1511.08734,
  title  = {A class of cyclic $(v;k_1,k_2,k_3;\lambda)$ difference families with $v \equiv 3 \pmod{4}$ a prime},
  author = {Dragomir Z. Djokovic and Ilias S. Kotsireas},
  journal= {arXiv preprint arXiv:1511.08734},
  year   = {2017}
}

Comments

11 pages, 1 table. Updated version

A class of cyclic $(v;k_1,k_2,k_3;\lambda)$ difference families with $v \equiv 3 \pmod{4}$ a prime

Abstract

Keywords

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