DocumentCode
1266170
Title
NMDS codes of maximal length over Fq,8⩽q⩽11
Author
Marcugini, Stefano ; Milani, Alfredo ; Pambianco, Fernanda
Author_Institution
Dept. of Math. & Informatics, Perugia Univ., Italy
Volume
48
Issue
4
fYear
2002
fDate
4/1/2002 12:00:00 AM
Firstpage
963
Lastpage
966
Abstract
A linear [n,k,d]q code C is called near maximum-distance separable (NMDS) if d(C)=n-k and d(C⊥)=k. The maximum length of an NMDS [n,k,d]q code is denoted by m´(k,q). In this correspondence, it has been verified by a computer-based proof that m´(5,8)=15, m´(4,9)=16,m´(5,9)=16, and 20⩽m´(4,11)⩽21. Moreover, the NMDS codes of length m´(4,8), m´(5,8), and m´(4,9) have been classified. As the dual code of an NMDS code is NMDS, the values of m´(k,8), k=10,11,12, and of m´(k,9),k=12,13,14 have been also deduced
Keywords
dual codes; linear codes; Galois fields; NMDS codes; computer-based proof; dual code; linear code; maximum length; near maximum-distance separable codes; Galois fields; Hamming distance; Informatics; Linear code; Mathematics; Parity check codes; Vectors;
fLanguage
English
Journal_Title
Information Theory, IEEE Transactions on
Publisher
ieee
ISSN
0018-9448
Type
jour
DOI
10.1109/18.992802
Filename
992802
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