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".
Copyrights notice
The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. Copyrights notice
이전에는 1점 대수 기하학(AG) 코드에 대한 빠른 일반화 최소 거리(GMD) 디코딩 알고리즘을 제공했습니다. 본 논문에서는 이들 코드에 대한 또 다른 고속 GMD 디코딩 알고리즘을 제안하는데, 여기서 현재 방법은 삭제 삭제 절차를 포함하고 과거 방식은 삭제 추가 절차를 사용한다. 두 가지 방법 모두 주어진 신드롬 배열의 최소 다항식 집합을 찾습니다. 이는 각 크기의 삭제 위치 지정자 집합으로 제한된 삭제 및 오류 위치 지정자 다항식 집합의 후보입니다. RS 코드와 같은 1차원 대수 부호에 대해서는 소거 추가 및 삭제 GMD 복호 알고리즘이 모두 확립되어 있지만, 1점 AG 코드와 같은 다차원 대수 부호에 대해서는 소거 추가 GMD 복호 알고리즘만 제시되어 있다. 현재 삭제 삭제 GMD 디코딩 알고리즘은 제한된 다차원 시프트 레지스터 합성의 관점에서 BMS(Berlekamp-Massey-Sakata) 알고리즘을 기반으로 합니다. 과거와 현재의 방법 모두 오류 정정 범위까지 1포인트 AG 코드를 디코딩하는 데 공동 역할을 할 것으로 예상됩니다.
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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},}
부
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 -