Art

J-GLOBAL ID：201602209209511855   Reference number：16A0273133

Decoding of Projective Reed-Muller Codes by Dividing a Projective Space into Affine Spaces

射影空間のアフィン空間への分割による射影Reed-Muller符号の復号化

Author (2)： NAKASHIMA Norihiro (Toyota Technological Inst.) ,  MATSUI Hajime (Toyota Technological Inst.)
Material： IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences (Web)  (IEICE Trans Fundam Electron Commun Comput Sci (Web))
Volume： E99.A  Issue： 3  Page： 733-741 (J-STAGE)  Publication year： 2016 
JST Material Number： U0466A  ISSN： 1745-1337  Document type： Article
Article type： 原著論文  Country of issue： Japan (JPN)  Language： ENGLISH (EN)

Thesaurus term： mathematical space ,  division and resolution ,  *Reed-Muller code ,  basis ,  Fourier transformation ,  distance ,  code distance ,  *sequential decoding ,  algorithm ,  computational complexity ,  *error correcting capability ,  error rate
Semi thesaurus term： *projective space ,  affine space ,  space division ,  Groebner base ,  discrete Fourier transformation ,  self-dual codes ,  minimum distance ,  *signal processing algorithms ,  code term

JST classification (1)： Code theory  (ND02030R)

Reference (27)：

• [1] G. Lachaud, “Projective Reed-Muller codes,” Coding Theory and Applications, Lecture Notes in Computer Science, vol.311, pp.125-129, Springer Berlin Heidelberg, Berlin, Heidelberg, 1988.
• [2] A.B. Sorensen, “Projective Reed-Muller codes,” IEEE Trans. Inf. Theory, vol.37, no.6, pp.1567-1576, Nov. 1991.
• [3] T.P. Berger and L. de Maximy, “Cyclic projective Reed-Muller codes,” Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, Lecture Notes in Computer Science, vol.2227, pp.77-81, Springer Berlin Heidelberg, Berlin, Heidelberg, 2001.
• [4] S. Ballet and R. Rolland, “On low weight codewords of generalized affine and projective Reed-Muller codes,” Des. Codes Cryptogr., vol.73, no.2, pp.271-297, Nov. 2014.
• [5] A. Dür, “The decoding of extended Reed-Solomon codes,” Discrete Math., vol.90, no.1, pp.21-40, June 1991.

Terms in the title (5)： 射影空間 ,  アフィン空間 ,  射影 ,  Reed-Muller符号 ,  復号化