English

On abelian $(2^{2m+1}(2^{m-1}+1), 2^m(2^m+1), 2^m)$-difference sets

Combinatorics 2007-05-23 v1 Number Theory

Abstract

In this paper we prove that an abelian group contains (22m+1(2m1+1),2m(2m+1),2m)(2^{2m+1}(2^{m-1}+1), 2^m(2^m+1), 2^m)-difference sets with m3m\geqslant 3 if and only if it contains an elementary abelian 2-group of order 22m2^{2m}. Our proof shows that the method of constructing such difference sets is essentially unique.

Cite

@article{arxiv.math/0508086,
  title  = {On abelian $(2^{2m+1}(2^{m-1}+1), 2^m(2^m+1), 2^m)$-difference sets},
  author = {K. T. Arasu and Yu Qing Chen and Alexander Pott},
  journal= {arXiv preprint arXiv:math/0508086},
  year   = {2007}
}

Comments

18 pages

R2 v1 2026-07-22T17:22:48.782Z