cyclic vector 中文意思是什麼
cyclic vector
解釋
循環向量-
By initiating the values of vector description for a primitive element, all finite field elements could be generated by continue cyclic shifting, gmw sequences then could be generated by trace function calculation
通過預置本原元向量表達的初始值，不斷的進行向量循環移位來生成有限域中的元素。生成有限域中所有元素后，即可按跡函數計算出gmw序列。 -
The main contributions of the second part of this dissertation are focused on the cryptographic properties of logical functions over finite field, with the help of the properties of trace functions, and that of p - polynomials, as well as the permutation theory over finite field : the new definition of chrestenson linear spectrum is given and the relation between the new chrestenson linear spectrum and the chrestenson cyclic spectrum is presented, followed by the inverse formula of logical function over finite field ; the distribution for linear structures of the logical functions over finite field is discussed and the complete construction of logical functions taking on all vectors as linear structures is suggested, which leads to the conception of the extended affine functions over finite field, whose cryptographic properties is similar to that of the affine functions over field gf ( 2 ) and prime field fp ; the relationship between the degeneration of logical functions and the linear structures, the degeneration of logical functions and the support of chrestenson spectrum, as well as the relation between the nonlinearity and the linear structures are discussed ; using the relation of the logical functions over finite field and the vector logical functions over its prime field, we reveal the relationship between the perfect nonlinear functions over finite field and the vector generalized bent functions over its prime field ; the existence or not of the perfect nonlinear functions with any variables over any finite fields is offered, and some methods are proposed to construct the perfect nonlinear functions by using the balanced p - polynomials over finite field
重新定義了有限域上邏輯函數的chrestenson線性譜，考察了新定義的chrestenson線性譜和原來的chrestenson循環譜的關系，並利用一組對偶基給出了有限域上邏輯函數的反演公式；給出了有限域上隨機變量聯合分佈的分解式，並利用隨機變量聯合分佈的分解式對有限域上邏輯函數的密碼性質進行了研究；給出了有限域上邏輯函數與相應素域上向量邏輯函數的關系，探討了它們之間密碼性質的聯系，如平衡性，相關免疫性，擴散性，線性結構以及非線性度等；討論了有限域上邏輯函數各類線性結構之間的關系，並給出了任意點都是線性結構的邏輯函數的全部構造，由此引出了有限域上的「泛仿射函數」的概念；考察了有限域上邏輯函數的退化性與線性結構的關系、退化性與chrestenson譜支集的關系；給出了有限域邏輯函數非線性度的定義，利用有限域上邏輯函數的非線性度與相應素域上向量邏輯函數非線性度的關系，考察了有限域上邏輯函數的非線性度與線性結構的關系；利用有限域上邏輯函數與相信息工程大學博士學位論文應素域上向量邏輯函數的關系，揭示了有限域上的廣義bent函數與相應素域上的廣義bent函數的關系，以及有限域上的完全非線性函數與相應素域上向量廣義bent函數之間的關系;給出了任意有限域上任意。 -
In the third part, i genelized one theorem of lambert ' s from a hilbert space to a semi - self - conjugate vector space, and some results of reflexivity are attained. in the fourth part, i discussed the algebraic reflexivity of a ( strictly ) cyclic linear transformation on a vector space
1 ，把這個結論從hilbert空間推廣到半自共軛的banach空間，得出一些自反性的結論；第4章討論了線性空間上的（嚴格）循環的線性變換的代數性自反。 -
I also introduce how the author came up with the thoughts of the thesis and the main results. in the second part, i discussed some properties regarding the reflexivity of cyclic subalgebras on a normed vector space. the 2 - refiexivity and hyporeflexivity of cyclic subalgebras are attained, and the answers to deddens ' s questions in reference document [ 19 ] are obtained partly
第1章介紹了自反代數的發展概述及問題的提出，以及本論文的主要內容；第2章討論了循環運算元代數的2 -自反性和亞自反性以及其它一些與自反性相關的性質，並且部分地回答了deddens的問題：第3章推廣（ alanlambert的）定理1
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