The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. ex. Some numerals are expressed as "XNUMX".
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The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. Copyrights notice
Pour les codes cycliques, certaines limites inférieures bien connues et certaines méthodes de décodage allant jusqu'à la moitié des limites sont suggérées. En particulier, la limite de décalage constitue une bonne limite inférieure de la distance minimale pour les codes cycliques, les codes de Reed-Muller et les codes géométriques de Goppa. Dans cet article, nous considérons les codes cycliques définis par leur ensemble de définition, et une nouvelle dérivation simple de la limite de décalage utilisant la transformée de Fourier discrète avec des éléments inconnus et le théorème de Blahut est présentée. De plus, deux exemples de codes cycliques binaires sont donnés.
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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 -