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 a...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.展开更多
基金financially supported by the TAMOP-4.2.1/B-09/1/KONV-2010-0005 project
文摘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.
