IEICE TRANSACTIONS on Fundamentals
Decoding of Projective Reed-Muller Codes by Dividing a Projective Space into Affine Spaces
Summary :
A projective Reed-Muller (PRM) code, obtained by modifying a Reed-Muller code with respect to a projective space, is a doubly extended Reed-Solomon code when the dimension of the related projective space is equal to 1. The minimum distance and the dual code of a PRM code are known, and some decoding examples have been presented for low-dimensional projective spaces. In this study, we construct a decoding algorithm for all PRM codes by dividing a projective space into a union of affine spaces. In addition, we determine the computational complexity and the number of correctable errors of our algorithm. Finally, we compare the codeword error rate of our algorithm with that of the minimum distance decoding.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E99-A No.3 pp.733-741
- Publication Date
- 2016/03/01
- Publicized
- Online ISSN
- 1745-1337
- DOI
- 10.1587/transfun.E99.A.733
- Type of Manuscript
- PAPER
- Category
- Coding Theory
Authors
Norihiro NAKASHIMA
Toyota Technological Institute
Hajime MATSUI
Toyota Technological Institute
Keyword
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Norihiro NAKASHIMA, Hajime MATSUI, "Decoding of Projective Reed-Muller Codes by Dividing a Projective Space into Affine Spaces" in IEICE TRANSACTIONS on Fundamentals,
vol. E99-A, no. 3, pp. 733-741, March 2016, doi: 10.1587/transfun.E99.A.733.
Abstract: A projective Reed-Muller (PRM) code, obtained by modifying a Reed-Muller code with respect to a projective space, is a doubly extended Reed-Solomon code when the dimension of the related projective space is equal to 1. The minimum distance and the dual code of a PRM code are known, and some decoding examples have been presented for low-dimensional projective spaces. In this study, we construct a decoding algorithm for all PRM codes by dividing a projective space into a union of affine spaces. In addition, we determine the computational complexity and the number of correctable errors of our algorithm. Finally, we compare the codeword error rate of our algorithm with that of the minimum distance decoding.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E99.A.733/_p
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@ARTICLE{e99-a_3_733,
author={Norihiro NAKASHIMA, Hajime MATSUI, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Decoding of Projective Reed-Muller Codes by Dividing a Projective Space into Affine Spaces},
year={2016},
volume={E99-A},
number={3},
pages={733-741},
abstract={A projective Reed-Muller (PRM) code, obtained by modifying a Reed-Muller code with respect to a projective space, is a doubly extended Reed-Solomon code when the dimension of the related projective space is equal to 1. The minimum distance and the dual code of a PRM code are known, and some decoding examples have been presented for low-dimensional projective spaces. In this study, we construct a decoding algorithm for all PRM codes by dividing a projective space into a union of affine spaces. In addition, we determine the computational complexity and the number of correctable errors of our algorithm. Finally, we compare the codeword error rate of our algorithm with that of the minimum distance decoding.},
keywords={},
doi={10.1587/transfun.E99.A.733},
ISSN={1745-1337},
month={March},}
Copy
TY - JOUR
TI - Decoding of Projective Reed-Muller Codes by Dividing a Projective Space into Affine Spaces
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 733
EP - 741
AU - Norihiro NAKASHIMA
AU - Hajime MATSUI
PY - 2016
DO - 10.1587/transfun.E99.A.733
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E99-A
IS - 3
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - March 2016
AB - A projective Reed-Muller (PRM) code, obtained by modifying a Reed-Muller code with respect to a projective space, is a doubly extended Reed-Solomon code when the dimension of the related projective space is equal to 1. The minimum distance and the dual code of a PRM code are known, and some decoding examples have been presented for low-dimensional projective spaces. In this study, we construct a decoding algorithm for all PRM codes by dividing a projective space into a union of affine spaces. In addition, we determine the computational complexity and the number of correctable errors of our algorithm. Finally, we compare the codeword error rate of our algorithm with that of the minimum distance decoding.
ER -
English
