Weight Distributions of Linear Codes from Perfect Nonlinear Functions of Dembowski-Ostrom Type
Li Ping, Yue Zhou · 2010
Perfect nonlinear functions of Dembowski-Ostrom type is the main type of perfect nonlinear functions. Only one class of perfect nonlinear functions does not belong to the Dembowski-Ostrom type.We first give the definition of the perfect nonlinear functions of Dembowski-Ostrom type,and generalize the construction of two linear codes to this type.We then show connection between this type of functions and the nondegenerate quadratic forms over finite fields.We also summarize properties of the preimage distributions of the quadratic forms.Based on the theory of quadratic forms and exponential sums,we determine the weight distributions of two classes of linear codes from all perfect nonlinear functions of the Dembowski-Ostrom type using a unified approach.