On the covering structures of two classes of linear codes from perfect nonlinear functions
IEEE Transactions on Information Theory
On the weight distribution of a class of cyclic codes
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 3
Proofs of two conjectures on ternary weakly regular bent functions
IEEE Transactions on Information Theory
Strongly regular graphs associated with ternary bent functions
Journal of Combinatorial Theory Series A
Cyclic codes and sequences: the generalized Kasami case
IEEE Transactions on Information Theory
Association schemes arising from bent functions
Designs, Codes and Cryptography
| Hi-index | 755.02 |
In this paper we present a unified way to determine the values and their multiplicities of the exponential sums SigmaxisinF(q)zetap Tr(af(x)+bx)(a,bisinFq,q=pm,pges3) for all perfect nonlinear functions f which is a Dembowski-Ostrom polynomial or p = 3,f=x(3(k)+1)/2 where k is odd and (k,m)=1. As applications, we determine (1) the correlation distribution of the m-sequence {alambda=Tr(gammalambda)}(lambda=0,1,...) and the sequence {blambda=Tr(f(gammalambda))}(lambda=0,1,...) over Fp where gamma is a primitive element of Fq and (2) the weight distributions of the linear codes over Fp defined by f.