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Construction of Independent Set and Its Application for Designed Minimum Distance
Junru ZHENG Takayasu KAIDA
Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Vol.E95A
No.12
pp.21072112 Publication Date: 2012/12/01
Online ISSN: 17451337
DOI: 10.1587/transfun.E95.A.2107
Print ISSN: 09168508 Type of Manuscript: Special Section PAPER (Special Section on Information Theory and Its Applications) Category: Coding Theory Keyword: discrete Fourier transform, independent set, shift bound, minimum distance, cyclic code,
Full Text: PDF>>
Summary:
The shift bound is a good lower bound of the minimum distance for cyclic codes, ReedMuller codes and geometric Goppa codes. It is necessary to construct the maximum value of the independent set. However, its computational complexity is very large. In this paper, we consider cyclic codes defined by their defining set, and a new method to calculate the lower bound of the minimum distance using the discrete Fourier transform (DFT) is shown. The computational complexity of this method is compared with the shift bound's one. Moreover construction of independent set is shown.

