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Higher-Order MDS Codes.
- Source :
-
IEEE Transactions on Information Theory . Dec2022, Vol. 68 Issue 12, p7798-7816. 19p. - Publication Year :
- 2022
-
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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00189448
- Volume :
- 68
- Issue :
- 12
- Database :
- Academic Search Index
- Journal :
- IEEE Transactions on Information Theory
- Publication Type :
- Academic Journal
- Accession number :
- 160651297
- Full Text :
- https://doi.org/10.1109/TIT.2022.3194521