Exponential Sums From Half Quadratic Forms and Their Applications

In this paper, we consider a class of exponential sums from some half quadratic binomials. The exponential sums are proven to be eleven-valued with maximal magnitude except for the trivial value . As applications, first, we investigate the autocorrelation and cross-correlation distribution among the sequences in a sequence family. Second, we determine the weight distributions of several classes of linear codes. Some of the dual codes have minimum distance four, which are optimal with respect to the Hamming bound. Our results extend the result by Choi et al. and show that some correlation values in it do not occur.