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.E95-A   No.12   pp.2107-2112
Publication Date: 2012/12/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E95.A.2107
Print ISSN: 0916-8508
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,  

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Summary: 
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. 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.