A Fast Erasure Deletion Generalized Minimum Distance Decoding for One-Point Algebraic-Geometry Codes

Masaya FUJISAWA; Shojiro SAKATA

A Fast Erasure Deletion Generalized Minimum Distance Decoding for One-Point Algebraic-Geometry Codes

Masaya FUJISAWA, Shojiro SAKATA

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Before we gave a fast generalized minimum distance (GMD) decoding algorithm for one-point algebraic-geometry (AG) codes. In this paper, we propose another fast GMD decoding algorithm for these codes, where the present method includes an erasure deletion procedure while the past one uses an erasure addition procedure. Both methods find a minimal polynomial set of a given syndrome array, which is a candidate for an erasure-and-error locator polynomial set constrained with an erasure locator set of each size. Although both erasure addition and deletion GMD decoding algorithms have been established for one-dimensional algebraic codes such as RS codes, nothing but the erasure addition GMD decoding algorithm for multidimensional algebraic codes such as one-point AG codes have been given. The present erasure deletion GMD decoding algorithm is based on the Berlekamp-Massey-Sakata (BMS) algorithm from the standpoint of constrained multidimensional shift register synthesis. It is expected that both our past and present methods play a joint role in decoding for one-point AG codes up to the error correction bound.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E84-A No.10 pp.2376-2382

Publication Date: 2001/10/01

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Type of Manuscript: Special Section PAPER (Special Section on Information Theory and Its Applications)

Category: Coding Theory

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Masaya FUJISAWA, Shojiro SAKATA, "A Fast Erasure Deletion Generalized Minimum Distance Decoding for One-Point Algebraic-Geometry Codes" in IEICE TRANSACTIONS on Fundamentals, vol. E84-A, no. 10, pp. 2376-2382, October 2001, doi: .
Abstract: Before we gave a fast generalized minimum distance (GMD) decoding algorithm for one-point algebraic-geometry (AG) codes. In this paper, we propose another fast GMD decoding algorithm for these codes, where the present method includes an erasure deletion procedure while the past one uses an erasure addition procedure. Both methods find a minimal polynomial set of a given syndrome array, which is a candidate for an erasure-and-error locator polynomial set constrained with an erasure locator set of each size. Although both erasure addition and deletion GMD decoding algorithms have been established for one-dimensional algebraic codes such as RS codes, nothing but the erasure addition GMD decoding algorithm for multidimensional algebraic codes such as one-point AG codes have been given. The present erasure deletion GMD decoding algorithm is based on the Berlekamp-Massey-Sakata (BMS) algorithm from the standpoint of constrained multidimensional shift register synthesis. It is expected that both our past and present methods play a joint role in decoding for one-point AG codes up to the error correction bound.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e84-a_10_2376/_p

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@ARTICLE{e84-a_10_2376,
author={Masaya FUJISAWA, Shojiro SAKATA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={A Fast Erasure Deletion Generalized Minimum Distance Decoding for One-Point Algebraic-Geometry Codes},
year={2001},
volume={E84-A},
number={10},
pages={2376-2382},
abstract={Before we gave a fast generalized minimum distance (GMD) decoding algorithm for one-point algebraic-geometry (AG) codes. In this paper, we propose another fast GMD decoding algorithm for these codes, where the present method includes an erasure deletion procedure while the past one uses an erasure addition procedure. Both methods find a minimal polynomial set of a given syndrome array, which is a candidate for an erasure-and-error locator polynomial set constrained with an erasure locator set of each size. Although both erasure addition and deletion GMD decoding algorithms have been established for one-dimensional algebraic codes such as RS codes, nothing but the erasure addition GMD decoding algorithm for multidimensional algebraic codes such as one-point AG codes have been given. The present erasure deletion GMD decoding algorithm is based on the Berlekamp-Massey-Sakata (BMS) algorithm from the standpoint of constrained multidimensional shift register synthesis. It is expected that both our past and present methods play a joint role in decoding for one-point AG codes up to the error correction bound.},
keywords={},
doi={},
ISSN={},
month={October},}

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TY - JOUR
TI - A Fast Erasure Deletion Generalized Minimum Distance Decoding for One-Point Algebraic-Geometry Codes
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 2376
EP - 2382
AU - Masaya FUJISAWA
AU - Shojiro SAKATA
PY - 2001
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E84-A
IS - 10
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - October 2001
AB - Before we gave a fast generalized minimum distance (GMD) decoding algorithm for one-point algebraic-geometry (AG) codes. In this paper, we propose another fast GMD decoding algorithm for these codes, where the present method includes an erasure deletion procedure while the past one uses an erasure addition procedure. Both methods find a minimal polynomial set of a given syndrome array, which is a candidate for an erasure-and-error locator polynomial set constrained with an erasure locator set of each size. Although both erasure addition and deletion GMD decoding algorithms have been established for one-dimensional algebraic codes such as RS codes, nothing but the erasure addition GMD decoding algorithm for multidimensional algebraic codes such as one-point AG codes have been given. The present erasure deletion GMD decoding algorithm is based on the Berlekamp-Massey-Sakata (BMS) algorithm from the standpoint of constrained multidimensional shift register synthesis. It is expected that both our past and present methods play a joint role in decoding for one-point AG codes up to the error correction bound.
ER -