Codes correcting restricted errors

Abstract

We study the largest possible length $B$ of $(B-1)$-dimensional linear codes over $\mathbb{F}_q$ which can correct up to $t$ errors taken from a restricted set $\mathcal{A}\subseteq \mathbb{F}_q^*$. Such codes can be applied to multilevel flash memories. Moreover, in the case that $q=p$ is a prime and the errors are limited by a constant we show that often the primitive $\ell$th roots of unity, where $\ell$ is a prime divisor of $p-1$, define good such codes.