On distances and self-dual codes over $F_q[u]/(u^t)$

Abstract

New metrics and distances for linear codes over the ring ${\mathbb{F}}_q\left[u\right]∕\left(u^t\right)$ are defined, which generalize the Gray map, Lee weight, and Bachoc weight; and new bounds on distances are given. Two characterizations of self-dual codes over ${\mathbb{F}}_q\left[u\right]∕\left(u^t\right)$ are determined in terms of linear codes over ${\mathbb{F}}_q$. An algorithm to produce such self-dual codes is also established.