This article presents new row-column twisted Reed-Solomon codes that exhibit MDS properties, indicating significant advancements in coding theory.
In this article, we present a new class of codes known as row-column twisted Reed-Solomon codes (abbreviated as RCTRS), motivated by the works of {beelen2017twisted} and {liu2025column}. We explicitly provide conditions for such codes to be MDS and also ensure their existence. By determining the dimensions of their Schur squares, we prove that these MDS codes are not equivalent to Reed-Solomon codes, thus presenting a new family of non-RS MDS codes. Additionally, we prove that these MDS codes are also not equivalent to column twisted Reed-Solomon codes described in {liu2025column}, showing the novelty of our construction.
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Bhagat et al. (2025) studied this question.
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