A Dual of Well-Behaving Type Designed Minimum Distance
Summary :
In this paper, we propose a lower bound for the minimum distance of [n,k] linear codes which are specified by generator matrices whose rows are k vectors of a given sequence of n linearly independent vectors over a finite field. The Feng-Rao bound and the order bound give the lower bounds for the minimum distance of the dual codes of the codes considered in this paper. We show that the proposed bound gives the true minimum distance for Reed-Solomon and Reed-Muller codes and exceeds the Goppa bound for some L-type algebraic geometry codes.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E84-A No.2 pp.647-652
- Publication Date
- 2001/02/01
- Publicized
- Online ISSN
- DOI
- Type of Manuscript
- PAPER
- Category
- Coding Theory
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Tomoharu SHIBUYA, Kohichi SAKANIWA, "A Dual of Well-Behaving Type Designed Minimum Distance" in IEICE TRANSACTIONS on Fundamentals,
vol. E84-A, no. 2, pp. 647-652, February 2001, doi: .
Abstract: In this paper, we propose a lower bound for the minimum distance of [n,k] linear codes which are specified by generator matrices whose rows are k vectors of a given sequence of n linearly independent vectors over a finite field. The Feng-Rao bound and the order bound give the lower bounds for the minimum distance of the dual codes of the codes considered in this paper. We show that the proposed bound gives the true minimum distance for Reed-Solomon and Reed-Muller codes and exceeds the Goppa bound for some L-type algebraic geometry codes.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e84-a_2_647/_p
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@ARTICLE{e84-a_2_647,
author={Tomoharu SHIBUYA, Kohichi SAKANIWA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={A Dual of Well-Behaving Type Designed Minimum Distance},
year={2001},
volume={E84-A},
number={2},
pages={647-652},
abstract={In this paper, we propose a lower bound for the minimum distance of [n,k] linear codes which are specified by generator matrices whose rows are k vectors of a given sequence of n linearly independent vectors over a finite field. The Feng-Rao bound and the order bound give the lower bounds for the minimum distance of the dual codes of the codes considered in this paper. We show that the proposed bound gives the true minimum distance for Reed-Solomon and Reed-Muller codes and exceeds the Goppa bound for some L-type algebraic geometry codes.},
keywords={},
doi={},
ISSN={},
month={February},}
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TY - JOUR
TI - A Dual of Well-Behaving Type Designed Minimum Distance
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 647
EP - 652
AU - Tomoharu SHIBUYA
AU - Kohichi SAKANIWA
PY - 2001
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E84-A
IS - 2
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - February 2001
AB - In this paper, we propose a lower bound for the minimum distance of [n,k] linear codes which are specified by generator matrices whose rows are k vectors of a given sequence of n linearly independent vectors over a finite field. The Feng-Rao bound and the order bound give the lower bounds for the minimum distance of the dual codes of the codes considered in this paper. We show that the proposed bound gives the true minimum distance for Reed-Solomon and Reed-Muller codes and exceeds the Goppa bound for some L-type algebraic geometry codes.
ER -
English
