Recently, linear codes constructed from defining sets have been studied widely and they have many applications. For an odd prime p, let q=pm\documentclass[12pt]{minimal}
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\begin{document}$$q=p^{m}$$\end{document} for a positive integer m and Trm\documentclass[12pt]{minimal}
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\begin{document}$$\mathrm {Tr}_{m}$$\end{document} the trace function from Fq\documentclass[12pt]{minimal}
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\begin{document}$$\mathbb {F}_{q}$$\end{document} onto Fp\documentclass[12pt]{minimal}
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\begin{document}$$\mathbb {F}_{p}$$\end{document}. In this paper, for a positive integer t, let D⊂Fqt\documentclass[12pt]{minimal}
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\begin{document}$$D\subset \mathbb {F}^{t}_{q}$$\end{document} and D={(x1,x2)∈(Fq∗)2:Trm(x1+x2)=0}\documentclass[12pt]{minimal}
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\begin{document}$$D=\{(x_{1},x_{2}) \in (\mathbb {F}_{q}^{*})^{2} : \mathrm {Tr}_{m}(x_{1}+x_{2})=0\}$$\end{document}, we define a p-ary linear code CD\documentclass[12pt]{minimal}
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\begin{document}$$\mathcal {C}_{D}$$\end{document} by CD=c(a1,a2):(a1,a2)∈Fq2,\documentclass[12pt]{minimal}
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\begin{document}$$\begin{aligned} \mathcal {C}_{D}=\left\{ \mathbf {c}(a_{1},a_{2}) : (a_{1},a_{2})\in \mathbb {F}^{2}_{q}\right\} , \end{aligned}$$\end{document}where c(a1,a2)=Trma1x12+a2x22(x1,x2)∈D.\documentclass[12pt]{minimal}
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\begin{document}$$\begin{aligned} \mathbf {c}(a_{1},a_{2})=\left( \mathrm {Tr}_{m}\left( a_{1}x^{2}_{1}+a_{2}x^{2}_{2}\right) \right) _{(x_{1},x_{2})\in D}. \end{aligned}$$\end{document}We compute the weight enumerators of the punctured codes CD\documentclass[12pt]{minimal}
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\begin{document}$$\mathcal {C}_{D}$$\end{document}.
