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.