ナガタ　キヨシ   永田　清   経営学部 経営学科   教授

■ 標題   A Family of Codes on Projective Surface

■ 概要   As an extension of Reed-Solomon Code, Goppa had proposed to use a family of fractional functions for constructing the so-called classical Goppa code in 1970. Goppa continued to investigate the relationship between error correcting codes and algebraic curves, and extended his idea to obtain the codes on algebraic curves. After the moment of his works, the research on algebraic geometric codes has been developed and several important results are published both in theoretical and in practical point of view. One of the most theoretical results in construction of code is codes on a projective scheme X over Fq dened using the germ map. In case of X being a projective surface, Hansen gave a lower bound of the minimum distance of codes dened on some irreducible curves with Fq-rational points. In this paper, we propose a concrete construction of that type of codes over the typical projective surface P2, then give the dimension and a lower bound of the minimum distance which is better than Hansen's estimation in some cases.   Shibaki K., Nagata K.   共著   Proceedings of the 13th International Workshop on Algebraic and Combinatorial Coding Theory   Institute of Mathematics and Informatics Bulgarian Academy of Sciences   pp.299-304   2012/06

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