Serre has obtained sharp estimates for the number of rational points on an algebraic curve over a finite field. In this paper we supplement his technique with divisibility properties for exponential sums to derive new bounds for exponential sums in one and several variables. The new bounds give us an improvement on previous bounds for the minimum distance of the duals of BCH codes. The divisibility properties also imply the existence of gaps in the weight distribution of certain cyclic codes, and in particular gives us that BCH codes are divisible (in the sense of H. N. Ward).
|Number of pages
|Applicable Algebra in Engineering, Communications and Computing
|Published - Mar 1994
- Bounds on the distance of cyclic codes
- Divisible codes
- Exponential sums