New Linear Codes and Algebraic Function Fields Over Finite Fields

摘要

In this correspondence, we present 129 new linear codes over $ {BBF }_{8}$ and $ {BBF }_{9}$ based on the construction by Xing and Niederreiter using algebraic function fields and places of small degrees. In addition, we construct some global function fields in which the number of rational places improves the lower bounds given by van der Geer and van der Vlugt.