Some New Results on Splitter Sets

Zuo Ye; Tao Zhang; Xiande Zhang; Gennian Ge

doi:10.1109/TIT.2019.2952370

Some New Results on Splitter Sets

Zuo Ye, Tao Zhang, Xiande Zhang, Gennian Ge

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

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 \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.

Original language	English
Article number	8894541
Pages (from-to)	2765-2776
Number of pages	12
Journal	IEEE Transactions on Information Theory
Volume	66
Issue number	5
DOIs	https://doi.org/10.1109/TIT.2019.2952370
State	Published - 1 May 2020
Externally published	Yes

Keywords

Cayley graph
Splitter set
flash memory
lattice tiling

ASJC Scopus subject areas

Information Systems
Computer Science Applications
Library and Information Sciences

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10.1109/TIT.2019.2952370

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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 \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.",

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AU - Ge, Gennian

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AB - 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 \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.

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Some New Results on Splitter Sets

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