IEICE TRANSACTIONS on Fundamentals
A Simple Proof of Horiguchi's Error-Value Formula in Decoding of Alternant Codes and Its Applications
Summary :
A direct short proof of Horiguchi's formula for error values in alternant codes is provided. Horiguchi's formula employs only output polynomials of Berlekamp-Massey algorithm, which has less computational complexity than extended Euclidean algorithm for decoding alternant codes. As an application of our proof, we provide an explicit formula for the generator and parity check matrices of alternant codes and their singly- and doubly-extended codes.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E92-A No.8 pp.2146-2150
- Publication Date
- 2009/08/01
- Publicized
- Online ISSN
- 1745-1337
- DOI
- 10.1587/transfun.E92.A.2146
- Type of Manuscript
- LETTER
- Category
- Coding Theory
Authors
Keyword
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Hajime MATSUI, "A Simple Proof of Horiguchi's Error-Value Formula in Decoding of Alternant Codes and Its Applications" in IEICE TRANSACTIONS on Fundamentals,
vol. E92-A, no. 8, pp. 2146-2150, August 2009, doi: 10.1587/transfun.E92.A.2146.
Abstract: A direct short proof of Horiguchi's formula for error values in alternant codes is provided. Horiguchi's formula employs only output polynomials of Berlekamp-Massey algorithm, which has less computational complexity than extended Euclidean algorithm for decoding alternant codes. As an application of our proof, we provide an explicit formula for the generator and parity check matrices of alternant codes and their singly- and doubly-extended codes.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E92.A.2146/_p
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@ARTICLE{e92-a_8_2146,
author={Hajime MATSUI, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={A Simple Proof of Horiguchi's Error-Value Formula in Decoding of Alternant Codes and Its Applications},
year={2009},
volume={E92-A},
number={8},
pages={2146-2150},
abstract={A direct short proof of Horiguchi's formula for error values in alternant codes is provided. Horiguchi's formula employs only output polynomials of Berlekamp-Massey algorithm, which has less computational complexity than extended Euclidean algorithm for decoding alternant codes. As an application of our proof, we provide an explicit formula for the generator and parity check matrices of alternant codes and their singly- and doubly-extended codes.},
keywords={},
doi={10.1587/transfun.E92.A.2146},
ISSN={1745-1337},
month={August},}
Copy
TY - JOUR
TI - A Simple Proof of Horiguchi's Error-Value Formula in Decoding of Alternant Codes and Its Applications
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 2146
EP - 2150
AU - Hajime MATSUI
PY - 2009
DO - 10.1587/transfun.E92.A.2146
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E92-A
IS - 8
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - August 2009
AB - A direct short proof of Horiguchi's formula for error values in alternant codes is provided. Horiguchi's formula employs only output polynomials of Berlekamp-Massey algorithm, which has less computational complexity than extended Euclidean algorithm for decoding alternant codes. As an application of our proof, we provide an explicit formula for the generator and parity check matrices of alternant codes and their singly- and doubly-extended codes.
ER -
English
