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A new construction of perfect nonlinear functions using Galois rings
Author(s) -
Feng Tao
Publication year - 2009
Publication title -
journal of combinatorial designs
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.618
H-Index - 34
eISSN - 1520-6610
pISSN - 1063-8539
DOI - 10.1002/jcd.20213
Subject(s) - mathematics , prime (order theory) , combinatorics , nonlinear system , composite number , function (biology) , discrete mathematics , pure mathematics , algorithm , physics , quantum mechanics , evolutionary biology , biology
For a prime p , we give a construction of perfect nonlinear functions from ℤ p 2nto ℤ p 2when either of the following conditions holds: (1) n ≥ p ; (2) n < p , and n is a composite number or is the sum of positive composite numbers. It follows that when n ≥12, there is a perfect nonlinear function from ℤ p 2nto ℤ p 2for any prime p . © 2009 Wiley Periodicals, Inc. J Combin Designs 17: 229‐239, 2009