Asymmetric Single Magnitude Four Error Correcting Codes

Derong Xie; Jinquan Luo

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arXiv · 1903.01148

Asymmetric Single Magnitude Four Error Correcting Codes

Derong Xie·Jinquan Luo

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Abstract

Limited magnitude asymmetric error model is well suited for flash memory. In this paper, we consider the construction of asymmetric codes correcting single error over $\mathbb{Z}_{2^{k}r}$ and which are based on so called $B_{1}[4](2^{k}r)$ set. In fact, we reduce the construction of a maximal size $B_{1}[4](2^{k}r)$ set for $k\geq3$ to the construction of a maximal size $B_{1}[4](2^{k-3}r)$ set. Finally, we give a explicit formula of a maximal size $B_{1}[4](4r)$ set and some lower bounds of a maximal size $B_{1}[4](2r)$ set. By computer searching up to $q\leq106$, we conjecture that those lower bounds are tight.

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Derong Xie, Jinquan Luo. 2019-03-04. Asymmetric Single Magnitude Four Error Correcting Codes. https://arxiv.org/abs/1903.01148

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