2025/07/09 by Yuan, Zhiyu, Feng, Rongquan, Ge, Gennian
#FOS: Computer and information sciences #Information Theory (cs.IT)
paper · doi:10.48550/arxiv.2507.06578
In this paper, the existence of perfect and quasi-perfect splitter sets in finite abelian groups is studied, motivated by their application in coding theory for flash memory storage. For perfect splitter sets we view them as splittings of ℤn, and using cyclotomic polynomials we derive a general condition for the existence of such splittings under certain circumstances. We further establish a relation between B[-k, k](q) and B[-(k-1), k+1](q) splitter sets, and give a necessary and sufficient condition for the existence of perfect B[-1, 5](q) splitter sets. Finally, two nonexistence results for quasi-perfect splitter sets are presented.