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

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.