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標題: 使用有限幾何建構循環置換碼
Construction of Cyclically Permutable Codes from Finite Geometry
作者: 陳俊叡
Jun-Rui Chen
關鍵字: 有限幾何;歐基里德幾;何投影幾何;循環置換碼;Finite geometry;Euclidean geometry;Projective geometry;cyclically permutable code
引用: [1]M. Kuribayashi, and H. Tanaka, 'How to Generate Cyclically Permutable Codes From Cyclic Codes,' IEEE Transactions on Information Theory, vol. 52, no. 10, pp. 4660 -4663, Oct. 2006. [2]Jyun-Jie Wang, and Chi-Yuan Lin, 'Finite Geometry Codes Based on Geometry Permutation Decoding,' 2016 International Symposium on Computer, Consumer and Control, pp. 1051-1054, Jul. 2016. [3]Heng Tang, Jun Xu,S. Lin, and K. A. S. Abdel-Ghaffar, 'Codes on Finite Geometries,' IEEE Transactions on Information Theory, vol. 51, no. 2, pp. 572-596, Feb. 2005. [4]V. C. da Rocha, and J. S. Lemos-Neto, 'New Cyclically Permutable Codes,' 2011 IEEE Information Theory Workshop, pp. 693-697, Oct. 2011.   [5]Samvel Martirosyan, A. J. Han Vinck, and Ashot N. Harutyunyan, 'On Optical Orthogonal, Cyclically Permutable, and Super Optical Orthogonal Codes,' 2007 IEEE International Symposium on Information Theory, pp. 2406-2410, Jun. 2007. [6]E. Gilbert, 'Cyclically Permutable Error-Correcting Codes,' IEEE Transactions on Information Theory, vol. 9, no. 3, pp. 175-182, Jul. 1963. [7]Shu Lin, and Daniel J. Costello, 'Error Control Coding: Fundamentals and Applications (Second Edition) ,' Pearson College Div, 2004. [8]William E. Ryan, and Shu Lin, 'Channel Codes: Classical and Modern,' Cambridge University Press, 2009. [9]T. L. Alderson, and Keith E. Mellinger, 'Constructions of Optical Orthogonal Codes from Finite Geometry,' SIAM Journal on Discrete Mathematics, vol. 21, no. 3, pp. 785-793, Jan. 2007. [10]F. R. K. Chung, J. A. Salehi, and V. K. Wei, 'Optical Orthogonal Codes: Design, Analysis and Applications,' IEEE Transactions on Information Theory, vol. 35, no. 3, pp. 595-604, May. 1989.
本論文將探討如何使用有限幾何(Finite geometry)中的歐基里德幾何(Euclidean geometry, EG)和投影幾何(Projective geometry, PG)來建構循環置換碼(cyclically permutable code, CPC)。相較於一般循環置換碼的造法,本篇論文的研究重點將著重於幾何學中點、線、面的概念,並探討其循環位移(cyclic shift)的特性,將其融入編碼的概念,從而建構出循環置換碼。

In this thesis, we will explore how to construct cyclically permytable code (CPC) using Euclidean geometry (EG) and Projective geometry (PG) in Finite geometry. Compared with the general way to construct cyclic permutable code, this thesis will focus on the concepts of points, lines and flats in geometry, and explore the characteristic of cyclic shift, combined with the concept of coding, then construct the cyclically permytable code.
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