Non-RS MDS Codes via Row-Column Twists

Abstract

This article introduces a new class of codes, called row-column twisted Reed--Solomon (RCTRS) codes, motivated by the constructions in (Beelen et al. \cite{beelen2017twisted}) and (Liu et al. \cite{liu2025column}). Explicit conditions under which RCTRS codes are MDS are established, and their existence is proved by algebraic techniques. By deriving lower bounds on the dimensions of their Schur squares, it is shown that these MDS codes, as well as their extended codes, are not equivalent to Reed--Solomon codes, and hence form new families of non-RS MDS codes. It is further proved that they are not equivalent to column twisted Reed--Solomon codes or their extended versions, and, when the hook lies strictly between the two extreme positions, are not equivalent to twisted Reed--Solomon codes with twist $t=1$ either. Introducing twists in both a row and a column therefore yields a family of MDS codes distinct from the previously known constructions.