关于M{<$}bius变换的计算
On the computation of the M{ö}bius transform
摘要：
M{<$}bius变换是到布尔世界的关键变换;它允许在真表和代数范式之间改变布尔表示。在这项工作中，我们介绍了一个新的代数观点，这种转换的基础上的多项式形式的布尔函数。看来，我们可以执行一个新的概念：M{<$}bius计算变量的变量和新的计算属性。因此，我们提出了新的算法，可以产生一个巨大的速度的M{<$}bius计算的子族布尔函数。此外，我们还直接计算了某些特殊布尔函数的M{<$}bius变换.最后，我们表明，其中一些汉明重量是直接相关的代数程度的具体因素。
英文摘要：
The M{ö}bius transform is a crucial transformation into the Boolean world; it allows to change the Boolean representation between the True Table and Algebraic Normal Form. In this work, we introduce a new algebraic point of view of this transformation based on the polynomial form of Boolean functions. It appears that we can perform a new notion: the M{ö}bius computation variable by variable and new computation properties. As a consequence, we propose new algorithms which can produce a huge speed up of the M{ö}bius computation for sub-families of Boolean function. Furthermore we compute directly the M{ö}bius transformation of some particular Boolean functions. Finally, we show that for some of them the Hamming weight is directly related to the algebraic degree of specific factors.
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