A Decoding Scheme for The \(4\)-Ary Lexicodes with \(d_m = 4\)

Abstract

In this paper, we are interested in lexicographic codes which are greedily constructed codes. For an arbitrary length \(n\), we shall find the basis of quaternary lexicographic codes, for short, lexicodes, with minimum distance \(d_m = 4\). Also, using a linear nim sum of some bases (such a vector is called the testing vector), its decoding algorithm will be found.