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 $B{1}4$ set for $a\geq4$ and $\gcd(r,6)=1$ to the construction of a maximal size $B_{1}4$ set. Further, we will show that maximal size $B_{1}4$ sets can be reduced to maximal size $B_{1}4$ sets. Finally, we give a lower bounds of maximal size $B_{1}4$ and $B_{1}4$ sets.