中文

Journal of Applied Sciences ›› 2010, Vol. 28 ›› Issue (5): 441-446.doi: 10.3969/j.issn.0255-8297.2010.05.001

• Communication Engineering •     Next Articles

Weight Distributions of Linear Codes from Perfect Nonlinear Functions of Dembowski-Ostrom Type

LI Ping1, LI Chao1;2, ZHOU Yue1   

  1. 1. Department of Mathematic and System Science, National University of Defense Technology,
    Changsha 410073, China
    2. State Key Laboratory of Information Security, Institute of Software,
    Chinese Academy of Sciences, Beijing 100190, China
  • Received:2010-06-10 Revised:2010-07-27 Online:2010-09-26 Published:2010-09-26

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Abstract:

Abstract: 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.

Key words: perfect nonlinear functions,, quadratic forms, , exponential sums,, linear codes, , weight distributions

CLC Number: