Affine equivalent classes of Boolean functions have many applications in modern cryptography and circuit design. Previous publications have shown that affine equivalence on the entire space of Boolean functions can be computed up to 10 variables, but not on the quotient Boolean function space modulo functions of different degrees. Computing the number of equivalent classes of cosets of Reed-Muller code \(\mathcal {R}(1,n)\) is equivalent to classifying Boolean functions modulo linear functions, which can be computed only when n ≤ 7. Based on the linear representation of the affine group \(\mathcal {A}\mathcal {G}{\mathscr{L}}(n,2)\) on the quotient space \(\mathcal {R}(s,n)/\mathcal {R}(k,n)\), we obtain a useful counting formula to compute the number of equivalent classes. Instead of computing the conjugacy classes and representatives directly in \(\mathcal {A}\mathcal {G}{\mathscr{L}}(n,2)\), we reduce the computation complexity by introducing an isomorphic permutation group P_n and performing the computation in P_n. With the proposed algorithm, the number of equivalent classes of cosets of R(1,n) can be computed up to 10 variables. Furthermore, the number of equivalent classes on \(\mathcal {R}(s,n)/\mathcal {R}(k,n)\) can also be computed when − 1 ≤ k < s ≤ n ≤ 10, which is a major improvement and advancement comparing to previous methods.

布尔函数的仿射等效类在现代密码学和电路设计中有许多应用。以前的出版物表明，布尔函数整个空间上的仿射等价关系最多可以计算10个变量，但商数不同的布尔函数空间模函数不能仿射等价。计算等价类的Reed-Muller码陪集的数目\（\ mathcal {R}（1，N）\）等效于布尔函数分类模线性函数，这只能当计算Ñ基于该≤7.商空间\ {\ mathcal {R}（s，n）/ \上仿射组\（\ mathcal {A} \ mathcal {G} {\ mathscr {L}}（n，2）\）的线性表示数学运算{R}（k，n）\），我们获得了一个有用的计数公式来计算等效类的数量。与其直接在\（\ mathcal {A} \ mathcal {G} {\ mathscr {L}}（n，2）\）中直接计算共轭类和表示，我们通过引入同构置换群P _n来降低计算复杂度并在P _n中执行计算。使用所提出的算法，可以计算多达10个变量的R（1，n）陪集的等效类的数量。此外，等价类的对数\（（S，N）\ mathcal {R} / \ mathcal {R}（K，N）\）也可被计算时- 1≤ ķ <小号≤ Ñ ≤10，与以前的方法相比是一个重大改进和进步。