linear permutation 中文意思是什麼
linear permutation
解釋
線性排列- linear : adj. 1. 線的，直線的。2. 長度的。3. 【數學】一次的，線性的。4. 【動、植】線狀的；細長的。5. 由線條組成的，以線條為主的，強調線條的。
- permutation : （數學中）排列變化，徹底改變
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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。 -
A selection method of serm factorizations for linear transforms is presented. it is discovered that the near optimal results are almost everywhere and when the factorization error is small, the closer the permutation matrices, the closer the results. according this fact, a local search is proposed that based near optimal factorization method which can obtain the near optimal results. moreover, this method convergence very fast, can usually obtain useful results by very limited iterations. it is tested lossless image coding with the selection results and good results is obtained
通過大量的實驗，發現serm分解的近似最優結果是大量存在的，而且這些近似最優結果的分佈是分散的，當分解結果的誤差度量比較小時的時候，有當置換矩陣相近時，分解結果的誤差也相近的實驗事實。基於此觀察結果，給出了基於局部搜索的serm分解的近似最優分解方法，可以得到非常接近最優分解的結果。 -
At the same time, a novel approach to construction of ldpc codes based on the permutation matrix was proposed which got a parity check matrix with the shortest girth is 6. these codes keep the advantage of linear encoding and become more flexible. simulations show that the performance of short length codes of this kind is as excellent as other ldpc codes
同時提出一種基於置換陣循環移位的構造方法，得到的校驗矩陣圍長至少為6 ，且保持編碼的線性復雜度，碼率靈活，模擬結果驗證了置換陣ldpc碼碼長較短時，在高斯通道下性能接近或超過現有其他構造方式的ldpc碼。
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