DocumentCode :
939211
Title :
Duadic Codes
Author :
Leon, Jeffrey S. ; Masley, John M. ; Pless, Vera
Volume :
30
Issue :
5
fYear :
1984
fDate :
9/1/1984 12:00:00 AM
Firstpage :
709
Lastpage :
714
Abstract :
A new family of binary cyclic 
and 
codes are introduced, which include quadratic residue (QR) codes when 
is prime. These codes are defined in terms of their idempotent generators, and they exist for all odd 
where each 
is a prime 
. Dual codes are identified. The minimum odd weight of a duadic code satisfies a square root bound. When equality holds in the sharper form of this bound, vectors of minimum weight hold a projective plane. The unique projective plane of order 8 is held by the minimum weight vectors in two inequivalent 
duadic codes. All duadic codes of length less than 
are identified, and the minimum weights of their extensions are given. One of the duadic codes of length 
has greater minimum weight than the QR code of that length.
and codes are introduced, which include quadratic residue (QR) codes when is prime. These codes are defined in terms of their idempotent generators, and they exist for all odd where each is a prime . Dual codes are identified. The minimum odd weight of a duadic code satisfies a square root bound. When equality holds in the sharper form of this bound, vectors of minimum weight hold a projective plane. The unique projective plane of order 8 is held by the minimum weight vectors in two inequivalent duadic codes. All duadic codes of length less than are identified, and the minimum weights of their extensions are given. One of the duadic codes of length has greater minimum weight than the QR code of that length.Keywords :
Cyclic coding; Dual coding; Residue coding; Binary sequences; Circuits; Computer science; Feedback; Mathematics; Notice of Violation; Shift registers; Statistics; Terminology;
fLanguage :
English
Journal_Title :
Information Theory, IEEE Transactions on
Publisher :
ieee
ISSN :
0018-9448
Type :
jour
DOI :
10.1109/TIT.1984.1056944
Filename :
1056944
Link To Document :
