Linear Codes on Nonsingular Curves are Better than Those on Singular Curves
Summary :
Recently, Miura introduced a construction method of one-point algebraic geometry codes on singular curves, which is regarded as a generalization of one on nonsingular curves, and enables us to construct codes on wider class of algebraic curves. However, it is still not clear whether there really exist singular curves on which we can construct good codes that are never obtained from nonsingular curves. In this paper, we show that for fixed designed minimum distance in a wide range, the dimension of codes on a singular curve is smaller than or equal to that of the codes on its normalization, and the number of check symbols of the former codes is larger than that of the latter codes. This implies the optimality of nonsingular curves for code construction.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E82-A No.4 pp.665-670
- Publication Date
- 1999/04/25
- Publicized
- Online ISSN
- DOI
- Type of Manuscript
- PAPER
- Category
- Information Theory and Coding Theory
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Ryutaroh MATSUMOTO, "Linear Codes on Nonsingular Curves are Better than Those on Singular Curves" in IEICE TRANSACTIONS on Fundamentals,
vol. E82-A, no. 4, pp. 665-670, April 1999, doi: .
Abstract: Recently, Miura introduced a construction method of one-point algebraic geometry codes on singular curves, which is regarded as a generalization of one on nonsingular curves, and enables us to construct codes on wider class of algebraic curves. However, it is still not clear whether there really exist singular curves on which we can construct good codes that are never obtained from nonsingular curves. In this paper, we show that for fixed designed minimum distance in a wide range, the dimension of codes on a singular curve is smaller than or equal to that of the codes on its normalization, and the number of check symbols of the former codes is larger than that of the latter codes. This implies the optimality of nonsingular curves for code construction.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e82-a_4_665/_p
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@ARTICLE{e82-a_4_665,
author={Ryutaroh MATSUMOTO, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Linear Codes on Nonsingular Curves are Better than Those on Singular Curves},
year={1999},
volume={E82-A},
number={4},
pages={665-670},
abstract={Recently, Miura introduced a construction method of one-point algebraic geometry codes on singular curves, which is regarded as a generalization of one on nonsingular curves, and enables us to construct codes on wider class of algebraic curves. However, it is still not clear whether there really exist singular curves on which we can construct good codes that are never obtained from nonsingular curves. In this paper, we show that for fixed designed minimum distance in a wide range, the dimension of codes on a singular curve is smaller than or equal to that of the codes on its normalization, and the number of check symbols of the former codes is larger than that of the latter codes. This implies the optimality of nonsingular curves for code construction.},
keywords={},
doi={},
ISSN={},
month={April},}
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TY - JOUR
TI - Linear Codes on Nonsingular Curves are Better than Those on Singular Curves
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 665
EP - 670
AU - Ryutaroh MATSUMOTO
PY - 1999
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E82-A
IS - 4
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - April 1999
AB - Recently, Miura introduced a construction method of one-point algebraic geometry codes on singular curves, which is regarded as a generalization of one on nonsingular curves, and enables us to construct codes on wider class of algebraic curves. However, it is still not clear whether there really exist singular curves on which we can construct good codes that are never obtained from nonsingular curves. In this paper, we show that for fixed designed minimum distance in a wide range, the dimension of codes on a singular curve is smaller than or equal to that of the codes on its normalization, and the number of check symbols of the former codes is larger than that of the latter codes. This implies the optimality of nonsingular curves for code construction.
ER -
English
