DocumentCode :
941319
Title :
On cyclic MDS codes of length q over GF(q) (Corresp.)
Author :
Roth, Ron M. ; Seroussi, Gadiel
Volume :
32
Issue :
2
fYear :
1986
fDate :
3/1/1986 12:00:00 AM
Firstpage :
284
Lastpage :
285
Abstract :
It is shown that a cyclic code 
of length 
over GF 
is the maximum distance separable if and only if either 
is a prime, in which case is equivalent, up to a coordinate permutation, to an extended Reed-Solomon code, or 
is a trivial code of dimension 
. Hence there exists a nontrivial cyclic extended Reed-Solomon code of length over GF if and only if is a prime.
of length over GF is the maximum distance separable if and only if either is a prime, in which case is equivalent, up to a coordinate permutation, to an extended Reed-Solomon code, or is a trivial code of dimension . Hence there exists a nontrivial cyclic extended Reed-Solomon code of length over GF if and only if is a prime.Keywords :
Cyclic coding; Reed-Solomon coding; Arithmetic; Computer science; Linear code; Polynomials; Reed-Solomon codes;
fLanguage :
English
Journal_Title :
Information Theory, IEEE Transactions on
Publisher :
ieee
ISSN :
0018-9448
Type :
jour
DOI :
10.1109/TIT.1986.1057151
Filename :
1057151
Link To Document :
