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Register a new userGeneralized Hamming weights of three classes of linear codes
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Gaopeng Jian
Publication date
2016
fields
Informatics Engineering
and research's language is
English
Authors
Gaopeng Jian
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The generalized Hamming weights of a linear code have been extensively studied since Wei first use them to characterize the cryptography performance of a linear code over the wire-tap channel of type II. In this paper, we investigate the generalized Hamming weights of three classes of linear codes constructed through defining sets and determine them partly for some cases. Particularly, in the semiprimitive case we solve an problem left in Yang et al. (IEEE Trans. Inf. Theory 61(9): 4905--4913, 2015).
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Linear codes have been an interesting topic in both theory and practice for many years. In this paper, a class of $q$-ary linear codes with few weights are presented and their weight distributions are determined using Gauss periods. Some of the linear codes obtained are optimal or almost optimal with respect to the Griesmer bound. As s applications, these linear codes can be used to construct secret sharing schemes with nice access structures.
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