arXiv subjects
Publications and source records attributed to Marcel van der Vlugt.
We study the distribution of the number of rational points in a family of curves over a finite field of characteristic 2. This distribution determines the coset weight distribution of a certain BCH code.
We construct an explicit asymptotically good tower of curves over the field with eight elements. Its limit is 3/2.
We give a method for constructing Kummer covers with many points over finite fields.
In this note is we exhibit an elementary method to construct explicitly curves over finite fields with many points. Despite its elementary character the method is very efficient and can be regarded as a partial substitute for the use of class field theory.
The weight hierarchy of generalized Reed-Muller codes over arbitrary finite fields was determined by Heijnen and Pellikaan. In this paper we produce curves over finite fields with many points which are closely related to this weight hierarchy.
In this paper we give several methods to construct curves over finite fields with many points and illustrate this with examples of the results.
We give a method to construct explicitly a supersingular curve of given genus g in characteristic 2.