arXiv subjects
Publications and source records attributed to Gaopeng Jian.
The generalized Hamming weights (GHWs) are fundamental parameters of linear codes. In this paper, we investigate the generalized Hamming weights of two classes of linear codes constructed from defining sets and determine them completely employing a number-theoretic approach.
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.
Linear codes with few weights have applications in secret sharing, authentication codes, association schemes and strongly regular graphs. In this paper, several classes of two-weight and three-weight linear codes are presented and their weight distributions are determined using Weil sums. Some of the linear codes obtained are optimal or almost optimal with respect to the Griesmer bound.
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).
Telecare medical information systems (TMIS) aim to provide healthcare services remotely. Efficient and secure mechanism for authentication and key agreement is required in order to guarantee the security and privacy of patients in TMIS.