A class of quadratic forms and the associated few-weight codes

In this paper, we first study the (non)-degeneracy of a class of quadratic forms. Then with a proper defining set determined by the given quadratic form, we construct a class of linear codes, decide their weight enumerators and show that they are two- or three-weight codes by using the Weil sums. Some of the punctured codes of the discussed linear codes are optimal or distance optimal to the Griesmer bound.