In [22], Kelan Ding and Cunsheng Ding presented a class of linear codes and determined their weight distributions. In this paper, we focus on the generalized Hamming weights of these codes. In order to do so, we study the quadratic forms over subspaces of finite field and obtain some interesting results about subspaces and their dual spaces. On this basis, we solve all the generalized Hamming w...

We prove matching direct and inverse theorems for (algebraic) polynomial approximation with doubling weights w having finitely many zeros and singularities (i.e., points where w becomes infinite) on an interval and not too “rapidly changing” away from these zeros and singularities. This class of doubling weights is rather wide and, in particular, includes the classical Jacobi weights, generaliz...