A Note on the Rank Bounded Distance and Its Algorithms for Cyclic Codes
Pure and Applied Mathematics Journal
Volume 4, Issue 2-1, March 2015, Pages: 36-41
Received: Dec. 22, 2014; Accepted: Jan. 30, 2015; Published: Feb. 11, 2015
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Authors
Takayasu Kaida, Department Information and Computer Sciences, Faculty of Humanity-Oriented Science and Engineering, Kinki University, Iizuka, Fukuoka, Japan
Junru Zheng, Department of Human Development, Faculty of Humanities, Kyushu Women’s University, Kitakyushu, Fukuoka, Japan
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Abstract
The minimum distance for linear codes is one of the important parameters. The shift bound is a good lower bound of the minimum distance for cyclic codes, Reed-Muller codes and geometric Goppa codes. It is necessary to construct the maximum value of the independent set for the calculation of the shift bound. However, its computational complexity is very large, because the construction of the independent set is not unique. The authors proposed an algorithm for calculation of the independent set using the discrete Fourier transform in 2010. In this paper we give simple modification and new recurrent algorithms to improve the original algorithm.
Keywords
Cyclic Code, Discrete Fourier Transform, Independent Set, Proposed Algorithm, Recurrent Algorithm, Shift Bound
To cite this article
Takayasu Kaida, Junru Zheng, A Note on the Rank Bounded Distance and Its Algorithms for Cyclic Codes, Pure and Applied Mathematics Journal. Special Issue: Abridging over Troubled Water---Scientific Foundation of Engineering Subjects. Vol. 4, No. 2-1, 2015, pp. 36-41. doi: 10.11648/j.pamj.s.2015040201.17
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