Systematic [n, n – 2] codes with capability of correcting single- and adjacent transposition errors

Single- and adjacent transposition errors are the typographic errors often made by human operators. 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 single- and adjacent transposition errors. As a result, we give constructions of some classes of codes with code length $n=\frac{1}{2}(p+1)$. To our knowledge, these codes are new in the literature. Interestingly, they are in general not cyclic, although they consist of a cyclic sub-class for $p\equiv1$ mod 4.