Asymmetric Single Magnitude Four Error Correcting Codes

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 $B{1}4$ set. In fact, we reduce the construction of a maximal size $B_{1}4$ set for $k\geq3$ to the construction of a maximal size $B_{1}4$ set. Finally, we give a explicit formula of a maximal size $B_{1}4$ set and some lower bounds of a maximal size $B_{1}4$ set. By computer searching up to $q\leq106$, we conjecture that those lower bounds are tight.