Linear Codes From Perfect Nonlinear Functions Over Finite Fields

In this paper, a class of p-ary 3-weight linear codes and a class of binary 2-weight linear codes are proposed respectively by virtue of the properties of the perfect nonlinear functions over F
_p(m)
and (m, s)-bent functions from F
_2(m)
to F
_2(s)
, where p is an odd prime and m, s are positive integers. The weight distributions are completely determined by the sign of the Walsh transform of weakly regular bent functions and the size of the preimage of the employed (m, s)-bent functions at the zero point, respectively. As a special case, a class of optimal linear codes meeting Griesmer bound is obtained from our construction.