Construction of Independent Set and Its Application for Designed Minimum Distance
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.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E95-A No.12 pp.2107-2112
- Publication Date
- 2012/12/01
- Publicized
- Online ISSN
- 1745-1337
- DOI
- 10.1587/transfun.E95.A.2107
- Type of Manuscript
- Special Section PAPER (Special Section on Information Theory and Its Applications)
- Category
- Coding Theory
Authors
Keyword
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Junru ZHENG, Takayasu KAIDA, "Construction of Independent Set and Its Application for Designed Minimum Distance" in IEICE TRANSACTIONS on Fundamentals,
vol. E95-A, no. 12, pp. 2107-2112, December 2012, doi: 10.1587/transfun.E95.A.2107.
Abstract: 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.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E95.A.2107/_p
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@ARTICLE{e95-a_12_2107,
author={Junru ZHENG, Takayasu KAIDA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Construction of Independent Set and Its Application for Designed Minimum Distance},
year={2012},
volume={E95-A},
number={12},
pages={2107-2112},
abstract={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.},
keywords={},
doi={10.1587/transfun.E95.A.2107},
ISSN={1745-1337},
month={December},}
Copy
TY - JOUR
TI - Construction of Independent Set and Its Application for Designed Minimum Distance
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 2107
EP - 2112
AU - Junru ZHENG
AU - Takayasu KAIDA
PY - 2012
DO - 10.1587/transfun.E95.A.2107
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E95-A
IS - 12
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - December 2012
AB - 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.
ER -
English
