关于二进制矩阵方程猜想的一类新解

A Sort of New Solution for the Conjecture of Binary Matrix Equation

摘要: 本文给出了二进制矩阵方程|E – 2A| = q满足猜想要求的四个通解，由此基础解衍生出不同的解，根据具体的q就能确定出不同的解个数的下限，在此基础上进一步研究解的性质，进而求出大部分的解。我们的结论推广了François Arnault等人在文[1]的结果，解决了François Arnault在文[2]中提出的猜想问题。

Abstract: In this paper, we give four general solutions satisfying the requirement of the conjecture for binary matrix equation |E – 2A| = q. Many distinct solutions can be derived from the base solution, and the lower bound of the number of solutions can be determined, given the integer q. Furthermore, we study the properties of these base solutions, and find most of the solutions. We extend the result of François Arnault’s paper [1], and solve the conjecture proposed by François Arnault proposed in [2].