DocumentCode :
77345
Title :
On the Covering Radius of First-Order Generalized Reed–Muller Codes
Author :
Leducq, E.
Author_Institution :
Inst. de Math. de Jussieu, Univ. Paris Diderot, Paris, France
Volume :
59
Issue :
3
fYear :
2013
fDate :
Mar-13
Firstpage :
1590
Lastpage :
1596
Abstract :
We generalize to any finite Fq fields a theorem about covering radius of codes of strength 2 proved by Helleseth and coworkers. Then,using this result and partial covering radius, we give bounds for the covering radius of first-order generalized Reed-Muller codes. Finally, using Magma, we get some improvements for F3.
Keywords :
Reed-Muller codes; first-order generalized Reed-Muller codes; partial covering radius; Binary codes; Frequency modulation; Hamming weight; Indexes; Kernel; Polynomials; Upper bound; Covering radius; generalized Reed–Muller codes;
fLanguage :
English
Journal_Title :
Information Theory, IEEE Transactions on
Publisher :
ieee
ISSN :
0018-9448
Type :
jour
DOI :
10.1109/TIT.2012.2230216
Filename :
6362214
Link To Document :
https://search.ricest.ac.ir/dl/search/defaultta.aspx?DTC=49&DC=77345
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