Codes from Surfaces with Small Picard Number

作     者：Little, John Schenck, Hal 

作者机构：Coll Holy Cross Dept Math & Comp Sci Worcester MA 01610 USA Iowa State Univ Dept Math Ames IA 50011 USA 

出 版 物：《SIAM JOURNAL ON APPLIED ALGEBRA AND GEOMETRY》 (Siam J. Appl. Algebr. Geom.)

年 卷 期：2018年第2卷第2期

页      面：242-258页

核心收录：

基　　金：NSF Direct For Mathematical & Physical Scien Division Of Mathematical Sciences Funding Source: National Science Foundation 

主　　题：error control code algebraic surface Picard number evaluation code 

摘      要：Extending work of M. Zarzar, we evaluate the potential of Goppa-type evaluation codes constructed from linear systems on projective algebraic surfaces with small Picard number. Putting this condition on the Picard number provides some control over the numbers of irreducible components of curves on the surface and hence over the minimum distance of the codes. We find that such surfaces do not automatically produce good codes;the sectional genus of the surface also has a major influence. Using that additional invariant, we derive bounds on the minimum distance under the assumption that the hyperplane section class generates the Neron-Severi group. We also give several examples of codes from such surfaces with minimum distance better than the best known bounds in Grassl s tables.