Some results on generalized strong external difference families

X. Lu; X. Niu; H. Cao

Some results on generalized strong external difference families

Combinatorics 2017-11-21 v5

Authors: X. Lu , X. Niu , H. Cao

Abstract

A generalized strong external difference family (briefly $(v, m; k_1,\dots,k_m; \lambda_1,\dots,\lambda_m)$ -GSEDF) was introduced by Paterson and Stinson in 2016. In this paper, we construct some new GSEDFs for $m=2$ and use them to obtain some results on graph decomposition. We also give some nonexistence results for GSEDFs. Especially, we prove that a $(v, 3;k_1,k_2,k_3; \lambda_1,\lambda_2,\lambda_3)$ -GSEDF does not exist when $k_1+k_2+k_3< v$ .

Cite

@article{arxiv.1709.02952,
  title  = {Some results on generalized strong external difference families},
  author = {X. Lu and X. Niu and H. Cao},
  journal= {arXiv preprint arXiv:1709.02952},
  year   = {2017}
}

Comments

generalized strong external difference family; difference set; character theory; graph decomposition; nonexistence

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