Abstract
Let \(\mathbb {F}_{q}\) be the finite field with \(q=p^{m}\) elements, where p is an odd prime and m is a positive integer. For a positive integer t, let \(D\subset \mathbb {F}^{t}_{q}\) and let \({\mathrm {Tr}}_{m}\) be the trace function from \(\mathbb {F}_{q}\) onto \(\mathbb {F}_{p}\). In this paper, let \(D=\{(x_{1},x_{2},\ldots ,x_{t}) \in \mathbb {F}_{q}^{t}\setminus \{(0,0,\ldots ,0)\} : {\mathrm {Tr}}_{m}(x_{1}+x_{2}+\cdots +x_{t})=0\},\) we define a p-ary linear code \(\mathcal {C}_{D}\) by
where
We shall present the complete weight enumerators of the linear codes \(\mathcal {C}_{D}\) and give several classes of linear codes with a few weights. This paper generalizes the results of Yang and Yao (Des Codes Cryptogr, 2016).
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The authors would like to express deepest thanks to the editor and the anonymous reviewers for their invaluable comments and suggestions to improve the quality of this paper. Without their careful reading and sophisticated advice, the paper would have never been developed like this.
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Communicated by T. Helleseth.
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Ahn, J., Ka, D. & Li, C. Complete weight enumerators of a class of linear codes. Des. Codes Cryptogr. 83, 83–99 (2017). https://doi.org/10.1007/s10623-016-0205-8
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DOI: https://doi.org/10.1007/s10623-016-0205-8