Semi-bent functions play an important role in symmetric ciphers and sequence designs. So far, there are few studies related to the construction of vectorial semi-bent functions even though lots of work has been done on single-output semi-bent functions. In this paper, three classes of balanced vectorial semi-bent functions are presented with varying cryptographic properties. The classes denoted \({{\mathcal {D}}}{{\mathcal {C}}}\) and \({{\mathcal {D}}}{{\mathcal {S}}}\) are constructed using disjoint codes and disjoint spectra functions, respectively. The former class has a useful provable property that its component functions do not admit linear structures. It is shown that the number of output bits of the constructed n-variable \({{\mathcal {D}}}{{\mathcal {C}}}\) and \({{\mathcal {D}}}{{\mathcal {S}}}\) vectorial functions can respectively reach \((n+1)/2\) and n/3. In addition, a construction method of semi-bent functions from \({\mathbb {F}}_2^{3n} \rightarrow {\mathbb {F}}_2^n\) by using almost bent (AB) functions on \({\mathbb {F}}_2^n\) is given.

半弯曲函数在对称密码和序列设计中起着重要作用。到目前为止，尽管在单输出半弯曲函数上已经做了大量工作，但与向量半弯曲函数的构建相关的研究很少。在本文中，提出了三类具有不同密码特性的平衡矢量半弯曲函数。表示\({{\mathcal {D}}}{{\mathcal {C}}}\)和\({{\mathcal {D}}}{{\mathcal {S}}}\) 的类被构造分别使用不相交代码和不相交谱函数。前一类有一个有用的可证明性质，即它的组成函数不允许线性结构。表明构造的n变量的输出位数\({{\mathcal {D}}}{{\mathcal {C}}}\)和\({{\mathcal {D}}}{{\mathcal {S}}}\)向量函数可以分别达到\((n+1)/2\)和n /3。此外，利用几乎弯曲（AB）函数在\ ({\mathbb {F}}_2^{3n} \rightarrow {\mathbb {F}}_2^n\) 上构造半弯曲函数的方法({\mathbb {F}}_2^n\)给出。