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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Bent function ： ウィキペディア英語版 Bent function In the mathematical field of combinatorics, a bent function is a special type of Boolean function. This means it takes several inputs and gives one output, each of which has two possible values (such as ''0'' and ''1'', or ''true'' and ''false''). The name is figurative. Bent functions are so called because they are as different as possible from all linear and affine functions, the simplest or "straight" functions. This makes the bent functions naturally hard to approximate. Bent functions were defined and named in the 1960s by Oscar Rothaus in research not published until 1976.〔 They have been extensively studied for their applications in cryptography, but have also been applied to spread spectrum, coding theory, and combinatorial design. The definition can be extended in several ways, leading to different classes of generalized bent functions that share many of the useful properties of the original. == Walsh transform == Bent functions are defined in terms of the Walsh transform. The Walsh transform of a Boolean function is the function $\backslash hat:\backslash Z\_2^n\; \backslash to\; \backslash Z$ given by :$\backslash hat(a)\; =\; \backslash sum\_$ where is the dot product in Z.〔 Alternatively, let and . Then and hence :$\backslash hat(a)\; =\; |S\_0(a)|\; -\; |S\_1(a)|\; =\; 2\; |S\_0(a)|\; -\; 2^n.$ For any Boolean function ''ƒ'' and the transform lies in the range :$-2^n\; \backslash leq\; \backslash hat(a)\; \backslash leq\; 2^n.$ Moreover, the linear function and the affine function correspond to the two extreme cases, since :$$ \hat_0(a) = 2^n,~ \hat_1(a) = -2^n. Thus, for each the value of $\backslash hat(a)$ characterizes where the function ''ƒ''(''x'') lies in the range from ''ƒ''0(''x'') to ''ƒ''1(''x''). 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Bent function」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.