Bent向量函数、编码与设计
Bent Vectorial Functions, Codes and Designs
摘要：
Bent函数，或等价地，初等阿贝尔群$(\gf(2^{2m}), +)$中的Hadamard差集，已被用来构造具有对称差性质的对称和拟对称设计.本文的主要目的是使用弯曲向量函数的一个双参数家庭的二元线性码，不满足条件的Assmus-Mattson定理，但仍然持有$2$ -设计的建设。本文给出了Bent向量函数的一个新的编码理论刻画。
英文摘要：
Bent functions, or equivalently, Hadamard difference sets in the elementary Abelian group $(\gf(2^{2m}), +)$, have been employed to construct symmetric and quasi-symmetric designs having the symmetric difference property. The main objective of this paper is to use bent vectorial functions for a construction of a two-parameter family of binary linear codes that do not satisfy the conditions of the Assmus-Mattson theorem, but nevertheless hold $2$-designs. A new coding-theoretic characterization of bent vectorial functions is presented.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
