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- W2238741512 abstract "Linear codes with a few weights have been widely investigated in recent years. However, most of these known linear codes were defined over a prime field. In this paper, we mainly use Gauss sums to represent the Hamming weights of a class of $q$-ary linear codes, where $q$ is a power of a prime. The lower bound of the minimum Hamming distance of the codes is obtained. And in some special cases, we evaluate the weight distributions of the linear codes based on semi-primitive Gauss sums and obtain some one-weight, two-weight linear codes. It is quite interesting that we find a few optimal codes achieving some certain bounds on linear codes. The linear codes in this paper can be used in secret sharing schemes, authentication codes and data storage systems." @default.
- W2238741512 created "2016-06-24" @default.
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- W2238741512 date "2015-11-06" @default.
- W2238741512 modified "2023-10-15" @default.
- W2238741512 title "Evaluation of the weight distribution of a class of linear codes based on semi-primitive Gauss sums" @default.
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