On the generalized Hamming weights of cyclic codes

We prove several results on the generalized Hamming weights (GHW's) of linear codes, particularly for cyclic codes. Based on these and previously known results, we give some efficient algorithms for computing GHW hierarchy of cyclic codes. We give complete weight hierarchy for each of the binar...

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Bibliographic Details
Published in:IEEE transactions on information theory 1997-01, Vol.43 (1), p.299-308
Main Authors: Janwa, H., Lal, A.K.
Format: Article
Language:English
Subjects:
Algorithms
Block codes
Codes
Cryptography
Decoding
Hamming weight
Independent component analysis
Information technology
Linear code
Mathematics
NP-hard problem
Physics
Wire
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Summary:We prove several results on the generalized Hamming weights (GHW's) of linear codes, particularly for cyclic codes. Based on these and previously known results, we give some efficient algorithms for computing GHW hierarchy of cyclic codes. We give complete weight hierarchy for each of the binary cyclic codes of odd lengths /spl les/31. A table of second and third GHW's of binary cyclic codes of odd lengths /spl les/57 is also presented. We have also computed the second GHW of all binary cyclic codes of length 63 and the third GHW of one code from each dimension.
ISSN:0018-9448
1557-9654
DOI:10.1109/18.567719