منابع مشابه
Self-dual bent functions
A bent function is called self-dual if it is equal to its dual. It is called anti-self-dual if it is equal to the complement of its dual. A spectral characterization in terms of the Rayleigh quotient of the Sylvester Hadamard matrix is derived. Bounds on the Rayleigh quotient are given for Boolean functions in an odd number of variables. An efficient search algorithm based on the spectrum of th...
متن کاملOn the dual of (non)-weakly regular bent functions and self-dual bent functions
For weakly regular bent functions in odd characteristic the dual function is also bent. We analyse a recently introduced construction of nonweakly regular bent functions and show conditions under which their dual is bent as well. This leads to the definition of the class of dual-bent functions containing the class of weakly regular bent functions as a proper subclass. We analyse self-duality fo...
متن کاملTowards the classification of self-dual bent functions in eight variables
In this paper, we classify quadratic and cubic self-dual bent functions in eight variables with the help of computers. There are exactly four and 45 non-equivalent self-dual bent functions of degree two and three, respectively. This result is achieved by enumerating all eigenvectors with±1 entries of the Sylvester Hadamard matrix with an integer programming algorithm based on lattice basis redu...
متن کاملFull characterization of generalized bent functions as (semi)-bent spaces, their dual, and the Gray image
In difference to many recent articles that deal with generalized bent (gbent) functions f : Z 2 → Zq for certain small valued q ∈ {4, 8, 16}, we give a complete description of these functions for both n even and odd and for any q = 2 in terms of both the necessary and sufficient conditions their component functions need to satisfy. This enables us to completely characterize gbent functions as a...
متن کاملBent Functions
Bent functions have connections into various areas of mathematics and computer science which makes them an interesting object to study. This thesis is meant as a comprehensive study summarizing many of the results published in the last 40 years. In the first chapter we will motivate the definition of bent functions before we discuss some basic properties in chapter 2. This is done with a specia...
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ژورنال
عنوان ژورنال: International Journal of Information and Coding Theory
سال: 2010
ISSN: 1753-7703,1753-7711
DOI: 10.1504/ijicot.2010.032864