Some classes of systematic polynomial codes correcting single- and adjacent transposition errors

摘要

In this paper, we use 2 check digits to construct systematic polynomial codes over F_P, where p is an odd prime, that correct all the singleand adjacent transposition errors (which are typographic errors often made by human operators). As a result, we give constructions of several classes of codes with code length n = ½ (p + 1) and ½ (p -1). In particular, the classes of codes with n = ½ (p + 1) are new to our knowledge; while for the class of codes with n = ½ (p -1), our construction provides a larger set of code candidates compared with the previous work.