Integer codes correcting single asymmetric errors

Abstract

This paper presents a class of integer codes capable of correcting single asymmetric errors. The presented codes are defined over the ring of integers modulo 2b– 1 and are constructed with the help of a computer. The results of an exhaustive search have shown that, for practical lengths up to 4096 bits, the proposed codes use the same number of check bits as the best systematic single asymmetric error-correcting codes (SAECCs). Besides this, it is found that for some lengths the presented codes are perfect. Finally, the paper shows that the encoding/decoding complexity of the proposed codes is notably lower than that of the best systematic SAECCs.