Twisted Reed-Solomon Codes

Abstract

We present a new general construction of MDS codes over a finite field $\mathbb{F}_q$. We describe two explicit subclasses which contain new MDS codes of length at least $q/2$ for all values of $q \ge 11$. Moreover, we show that most of the new codes are not equivalent to a Reed-Solomon code.

5 pages, accepted at IEEE International Symposium on Information Theory 2017