Codes correcting errors in the modulus metric, Lee metric, and operator errors (Q1895473)

The author presents a code construction that obtains \(t\)-error correcting codes in the modulus metric, which is defined for two vectors \(u,v \in \{0, \ldots, Q - 1\}^n\) by \(d_M (u,v) = \sum^n_{i = 1} |u_i - v_i |\). Furthermore he introduces a concept of metric homomorphism and shows the existence of such a homomorphism from the transposition metric to the Lee metric and the modulus metric. The transposition distance between two \(Q\)-ary vectors \(u\) and \(v\) of length \(n\) is -- if possible -- the minimum number of neighbour-transpositions that transform \(u\) to \(v\); otherwise the distance is set to \(\infty\). Additionally new code families are developed for the mentioned metrics.