Title :
Polynomials With Linear Structure and Maiorana–McFarland Construction
Author :
Charpin, Pascale ; Sarkar, Sumanta
Author_Institution :
SECRET Project-Team, INRIA Paris, Le Chesnay, France
fDate :
6/1/2011 12:00:00 AM
Abstract :
In this paper, we study permutation polynomials over the finite fields that have linear structures. We present some results on such a permutation which transforms a hyperplane to another hyperplane. We fully characterize the bilinear polynomial with linear structure. The most important result of this paper is to show the relation between a Maiorana-McFarland function with an affine derivative and a polynomial with a linear structure. Moreover, we highlight this result in the context of resilient functions which are based on Maiorana-McFarland construction.
Keywords :
Reed-Muller codes; affine transforms; bilinear systems; Maiorana-McFarland construction; affine derivative; bilinear polynomial; finite fields; linear structure; permutation polynomials; Boolean functions; Context; Kernel; Periodic structures; Polynomials; Terminology; Transforms; Bent function; Maiorana–McFarland function; bilinear permutation; linear space; linear structure; permutation polynomial; resilient function;
Journal_Title :
Information Theory, IEEE Transactions on
Conference_Location :
6/1/2011 12:00:00 AM
DOI :
10.1109/TIT.2011.2133690