Some New Results on Splitter Sets

Zuo Ye; Tao Zhang; Xiande Zhang; Gennian Ge

Some New Results on Splitter Sets

Information Theory 2019-11-06 v1 math.IT

Authors: Zuo Ye , Tao Zhang , Xiande Zhang , Gennian Ge

Abstract

Splitter sets have been widely studied due to their applications in flash memories, and their close relations with lattice tilings and conflict avoiding codes. In this paper, we give necessary and sufficient conditions for the existence of nonsingular perfect splitter sets, $B[-k_1,k_2](p)$ sets, where $0\le k_{1}\leq k_{2}=4$ . Meanwhile, constructions of nonsingular perfect splitter sets are given. When perfect splitter sets do not exist, we present four new constructions of quasi-perfect splitter sets. Finally, we give a connection between nonsingular splitter sets and Cayley graphs, and as a byproduct, a general lower bound on the maximum size of nonsingular splitter sets is given.

Keywords

sequence design

Cite

@article{arxiv.1911.01722,
  title  = {Some New Results on Splitter Sets},
  author = {Zuo Ye and Tao Zhang and Xiande Zhang and Gennian Ge},
  journal= {arXiv preprint arXiv:1911.01722},
  year   = {2019}
}

Comments

15 pages; accepted to IEEE Transaction on Information Theory

Some New Results on Splitter Sets

Abstract

Keywords

Cite

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