Correcting Codes for Asymmetric Single Magnitude Four Error

Abstract

An error model with asymmetric single magnitude four error is considered. This paper is about constructions of codes correcting single error over $\mathbb{Z}_{2^{a}3^{b}r}$. Firstly, we reduce the construction of a maximal size $B_{1}[4](2^{a}3^{b}r)$ set for $a\geq4$ and $\gcd(r,6)=1$ to the construction of a maximal size $B_{1}[4](2^{a-3}3^{b}r)$ set. Further, we will show that maximal size $B_{1}[4](8\cdot3^{b}r)$ sets can be reduced to maximal size $B_{1}[4](3^{b}r)$ sets. Finally, we give a lower bounds of maximal size $B_{1}[4](2r)$ and $B_{1}[4](2\cdot3^{b}r)$ sets.