IEICE TRANSACTIONS on Fundamentals
A Note on the Shift Bound for Cyclic Codes by the DFT
Summary :
For cyclic codes some well-known lower bounds and some decoding methods up to the half of the bounds are suggested. Particularly, the shift bound is a good lower bound of the minimum distance for cyclic codes, Reed-Muller codes and geometric Goppa codes. In this paper we consider cyclic codes defined by their defining set, and new simple derivation of the shift bound using the discrete Fourier transform with unknown elements and the Blahut theorem is shown. Moreover two examples of binary cyclic codes are given.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E93-A No.11 pp.1918-1922
- Publication Date
- 2010/11/01
- Publicized
- Online ISSN
- 1745-1337
- DOI
- 10.1587/transfun.E93.A.1918
- 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, "A Note on the Shift Bound for Cyclic Codes by the DFT" in IEICE TRANSACTIONS on Fundamentals,
vol. E93-A, no. 11, pp. 1918-1922, November 2010, doi: 10.1587/transfun.E93.A.1918.
Abstract: For cyclic codes some well-known lower bounds and some decoding methods up to the half of the bounds are suggested. Particularly, the shift bound is a good lower bound of the minimum distance for cyclic codes, Reed-Muller codes and geometric Goppa codes. In this paper we consider cyclic codes defined by their defining set, and new simple derivation of the shift bound using the discrete Fourier transform with unknown elements and the Blahut theorem is shown. Moreover two examples of binary cyclic codes are given.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E93.A.1918/_p
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@ARTICLE{e93-a_11_1918,
author={Junru ZHENG, Takayasu KAIDA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={A Note on the Shift Bound for Cyclic Codes by the DFT},
year={2010},
volume={E93-A},
number={11},
pages={1918-1922},
abstract={For cyclic codes some well-known lower bounds and some decoding methods up to the half of the bounds are suggested. Particularly, the shift bound is a good lower bound of the minimum distance for cyclic codes, Reed-Muller codes and geometric Goppa codes. In this paper we consider cyclic codes defined by their defining set, and new simple derivation of the shift bound using the discrete Fourier transform with unknown elements and the Blahut theorem is shown. Moreover two examples of binary cyclic codes are given.},
keywords={},
doi={10.1587/transfun.E93.A.1918},
ISSN={1745-1337},
month={November},}
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TY - JOUR
TI - A Note on the Shift Bound for Cyclic Codes by the DFT
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1918
EP - 1922
AU - Junru ZHENG
AU - Takayasu KAIDA
PY - 2010
DO - 10.1587/transfun.E93.A.1918
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E93-A
IS - 11
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - November 2010
AB - For cyclic codes some well-known lower bounds and some decoding methods up to the half of the bounds are suggested. Particularly, the shift bound is a good lower bound of the minimum distance for cyclic codes, Reed-Muller codes and geometric Goppa codes. In this paper we consider cyclic codes defined by their defining set, and new simple derivation of the shift bound using the discrete Fourier transform with unknown elements and the Blahut theorem is shown. Moreover two examples of binary cyclic codes are given.
ER -
English
