Linear Codes on Nonsingular Curves are Better than Those on Singular Curves
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概要
- 論文の詳細を見る
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.
- 社団法人電子情報通信学会の論文
- 1999-04-25
著者
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Matsumoto Ryutaroh
Department Of Communications And Integrated Systems Tokyo Institute Of Technology
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