Optimal, Systematic, $q$-Ary Codes Correcting All Asymmetric and Symmetric Errors of Limited Magnitude

摘要

Systematic q-ary (q > 2) codes capable of correcting all asymmetric errors of maximum magnitude l , where l ¿ q - 2, are given. These codes are shown to be optimal. Further, simple encoding/decoding algorithms are described. The proposed code can be modified to design codes correcting all symmetric errors of maximum magnitude l, where l ¿ (q-2)/2.