Complete weight enumerators of linear codes based on Weil sums

With a proper 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.