Complete Weight Enumerators of a Class of Linear Codes From Weil Sums

Abstract

By appropriately choosing a defining set, we define a class of linear codes and determine their complete weight enumerators and weight enumerators using Weil sums. They only have two or three nonzero weights, and some of them are optimal with respect to the Griesmer bound or Markus Grassl’s code tables. So they are suitable for applications in strongly regular graphs and secret sharing schemes.

Keywords

• Linear code
• complete weight enumerator
• Weil sum
• weight enumerator