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Discrete Dynamics in Nature and Society
Volume 2017 (2017), Article ID 9627840, 3 pages
https://doi.org/10.1155/2017/9627840
Research Article

Class of Quadratic Almost Bent Functions That Is EA-Inequivalent to Permutations

School of Mathematics and Systems Science, Beihang University, No. 37, Xueyuan Road, Haidian District, Beijing 100191, China

Correspondence should be addressed to Xinyang Zhang

Received 15 February 2017; Revised 9 April 2017; Accepted 11 April 2017; Published 13 August 2017

Academic Editor: Allan C. Peterson

Copyright © 2017 Xinyang Zhang and Meng Zhou. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The permutation relationship for the almost bent (AB) functions in the finite field is a significant issue. Li and Wang proved that a class of AB functions with algebraic degree 3 is extended affine- (EA-) inequivalent to any permutation. This study proves that another class of AB functions, which was developed in 2009, is EA-inequivalent to any permutation. This particular AB function is the first known quadratic class EA-inequivalent to permutation.