Lower bounds on the minimum distance in Hermitian one-point differential codes  

作　　者：KORCHMROS Gábor NAGY Gábor Pétery 

机构地区：[1]Dipartimento di Matematica e Informatica, Università della Basilicata [2]Bolyai Institute, University of Szeged

出　　处：《Science China Mathematics》2013年第7期1449-1455,共7页中国科学：数学（英文版）

基　　金：financially supported by the TAMOP-4.2.1/B-09/1/KONV-2010-0005 project

摘　　要：Korchmaros and Nagy [Hermitian codes from higher degree places. J Pure Appl Algebra, doi： 10. 1016/j.jpaa.2013.04.002, 2013] computed the Weierstrass gap sequence G（P） of the Hermitian function field Fq2 （H） at any place P of degree 3, and obtained an explicit formula of the Matthews-Michel lower bound on the minimum distance in the associated differential Hermitian code CΩ（D, mP） where the divisor D is, as usual, the sum of all but one 1-degree Fq2-rational places of Fq2 （H） and m is a positive integer. For plenty of values of m depending on q, this provided improvements on the designed minimum distance of CΩ（D, mP）. Further improvements from G（P） were obtained by Korchmaros and Nagy relying on algebraic geometry. Here slightly weaker improvements are obtained from G（P） with the usual function-field method depending on linear series, Riemann-Roch theorem and Weierstrass semigroups. We also survey the known results on this subject.Korchmáros and Nagy [Hermitian codes from higher degree places. J Pure Appl Algebra, doi: 10. 1016/j.jpaa.2013.04.002, 2013] computed the Weierstrass gap sequence G(P) of the Hermitian function field Fq2( H ) at any place P of degree 3, and obtained an explicit formula of the Matthews-Michel lower bound on the minimum distance in the associated differential Hermitian code CΩ(D, mP ) where the divisor D is, as usual, the sum of all but one 1-degree Fq2-rational places of Fq2( H ) and m is a positive integer. For plenty of values of m depending on q, this provided improvements on the designed minimum distance of CΩ(D, mP). Further improvements from G(P) were obtained by Korchmáros and Nagy relying on algebraic geometry. Here slightly weaker improvements are obtained from G(P) with the usual function-field method depending on linear series, Riemann-Roch theorem and Weierstrass semigroups. We also survey the known results on this subject.

关 键 词：AG code Weierstrass gap Hermitian curve 

分 类 号：O157.4[理学—数学]