Higher-Order MDS Codes

Ron M. Roth

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arXiv · 2111.03210

Higher-Order MDS Codes

Ron M. Roth

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Abstract

An improved Singleton-type upper bound is presented for the list decoding radius of linear codes, in terms of the code parameters [n,k,d] and the list size L. L-MDS codes are then defined as codes that attain this bound (under a slightly stronger notion of list decodability), with 1-MDS codes corresponding to ordinary linear MDS codes. Several properties of such codes are presented; in particular, it is shown that the 2-MDS property is preserved under duality. Finally, explicit constructions for 2-MDS codes are presented through generalized Reed-Solomon (GRS) codes.

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Ron M. Roth. 2021-11-05. Higher-Order MDS Codes. https://arxiv.org/abs/2111.03210

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