DocumentCode
1254289
Title
Cyclic subcodes of generalized Reed-Muller codes
Author
Moreno, O. ; Duursma, I.M. ; Cherdieu, J.-P. ; Edouard, A.
Author_Institution
Gauss Res. Lab., Puerto Rico Univ., Rio Piedras, Puerto Rico
Volume
44
Issue
1
fYear
1998
fDate
1/1/1998 12:00:00 AM
Firstpage
307
Lastpage
311
Abstract
We consider certain subcodes of generalized Reed-Muller (GRM) codes, which we call homogeneous generalized Reed-Muller (HRM) codes. In general, they have a much better minimum distance than the GRM codes. The parameters of HRM codes are related to those of projective Reed-Muller (PRM) codes. Unlike most PRM codes, punctured HRM codes are cyclic. Under the trace map, HRM codes map to binary codes. These are in general much larger than classical RM codes, for the same minimum distance
Keywords
Reed-Muller codes; cyclic codes; polynomials; HRM codes; binary codes; cyclic subcodes; generalized Reed-Muller codes; homogeneous generalized Reed-Muller codes; minimum distance; projective Reed-Muller codes; punctured codes; Binary codes; Cryptography; Decoding; Error correction codes; Hamming distance; Hamming weight; Human resource management; Information theory; Notice of Violation; Upper bound;
fLanguage
English
Journal_Title
Information Theory, IEEE Transactions on
Publisher
ieee
ISSN
0018-9448
Type
jour
DOI
10.1109/18.651056
Filename
651056
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