1. New Results on Asymmetric Single Correcting Codes of Magnitude Four.
- Author
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Xie, Derong and Luo, Jinquan
- Subjects
- *
FLASH memory , *MICROELECTROMECHANICAL systems , *NONVOLATILE memory , *ERROR-correcting codes - Abstract
An error model with asymmetric single error with magnitude four is considered. In this paper, the constructions of codes correcting single error of magnitude four over $\mathbb {Z}_{2^{{a}}3^{{b}}{r}}$ are studied which is equivalent to construct $B_{1}[{4}](2^{{a}}3^{{b}}{r})$ sets. Firstly, we reduce the construction of a maximal size ${B}_{1}[{4}](2^{{a}}3^{{b}}{r})$ set for ${a}\geq 4$ and $ \gcd ({r},6)=1$ to the construction of a maximal size ${B}_{1}[{4}](2^{{a}-3}3^{{b}}{r})$ set. Furthermore, we will show that maximal size ${B}_{1}[{4}](8\cdot 3^{{b}}{r})$ sets can be reduced to maximal size ${B}_{1}[{4}](3^{{b}}{r})$ sets and also give lower bounds of maximal size ${B}_{1}[{4}](12{r})$ and ${B}_{1}[{4}](2\cdot 3^{{b}}{r})$ sets. Finally, we give a necessary and sufficient condition on the existence of perfect ${B}_{1}[{4}]({p})$ set for prime $p$. [ABSTRACT FROM AUTHOR]
- Published
- 2021
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