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- W4288391452 abstract "An improved Singleton-type upper bound is presented for the list decoding radius of linear codes, in terms of the code parameters <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink> <tex-math notation=LaTeX>$[n,k,d]$ </tex-math></inline-formula> and the list size <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink> <tex-math notation=LaTeX>$L$ </tex-math></inline-formula> . <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink> <tex-math notation=LaTeX>$L$ </tex-math></inline-formula> -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." @default.
- W4288391452 created "2022-07-29" @default.
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- W4288391452 date "2022-12-01" @default.
- W4288391452 modified "2023-09-25" @default.
- W4288391452 title "Higher-Order MDS Codes" @default.
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- W4288391452 doi "https://doi.org/10.1109/tit.2022.3194521" @default.
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