DocumentCode
1443173
Title
On a family of Abelian codes and their state complexities
Author
Blackmore, Tim ; Norton, Graham H.
Author_Institution
Centre for Commun. Res., Bristol Univ., UK
Volume
47
Issue
1
fYear
2001
fDate
1/1/2001 12:00:00 AM
Firstpage
355
Lastpage
361
Abstract
We study Reed-Muller codes and “Berman” codes as Abelian codes. We show that the duals of Berman codes and Reed-Muller codes can be considered as belonging to the same family of Abelian codes. We also determine the minimum distance and state complexity of the duals of Berman codes. Each of the classical parameters generalizes that of Reed-Muller codes in the obvious way, but the state complexity does not. We conclude by comparing the asymptotic behavior of the state complexity of the duals of Berman codes with that of the obvious generalization of the state complexity of Reed-Muller codes
Keywords
Reed-Muller codes; binary codes; block codes; computational complexity; cyclic codes; dual codes; linear codes; Abelian codes; Berman codes; Reed-Muller codes; asymptotic behavior; binary linear block codes; cyclic codes; dual codes; minimum distance; state complexity; Codes; Councils; Decoding; Galois fields; Viterbi algorithm;
fLanguage
English
Journal_Title
Information Theory, IEEE Transactions on
Publisher
ieee
ISSN
0018-9448
Type
jour
DOI
10.1109/18.904535
Filename
904535
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