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Two general constructions of linear codes with functions over finite fieldshave been extensively studied in the literature. The first one is given by$\mathcal{C}(f)=\left\{ {\rm Tr}(af(x)+bx)_{x \in \mathbb{F}_{q^m}^*}: a,b \in\mathbb{F}_{q^m} \right\}$, where $q$ is a prime power, $\bF_{q^m}^*=\bF_{q^m}\setminus \{0\}$, $\tr$ is the trace function from $\bF_{q^m}$ to $\bF_q$, and$f(x)$ is a function from $\mathbb{F}_{q^m}$ to $\mathbb{F}_{q^m}$ with$f(0)=0$. Almost bent functions, quadratic functions and some monomials on$\bF_{2^m}$ were used in the first construction, and many families of binarylinear codes with few weights were obtained in the literature. This paperstudies some punctured codes of these binary codes. Several families of binarylinear codes with few weights and new parameters are obtained in this paper.Several families of distance-optimal binary linear codes with new parametersare also produced in this paper.

Some punctured codes of several families of binary linear codes