Classification of self dual quadratic bent functions

Authors:
Xiang-Dong Hou
Affiliations:
Department of Mathematics and Statistics, University of South Florida, Tampa, USA 33620
Venue:
Designs, Codes and Cryptography
Year:
2012

Citing 6
Cited 1

Topics in matrix analysis

Topics in matrix analysis
GL(m,2) acting on R(r,m)/R(r−1,m)

Discrete Mathematics
Finite fields

Finite fields
On the asymptotic number of inequivalent binary self-dual codes

Journal of Combinatorial Theory Series A
Self-dual bent functions

International Journal of Information and Coding Theory
Parametrization of self-dual codes by orthogonal matrices

Finite Fields and Their Applications

The selfnegadual properties of generalised quadratic Boolean functions

Designs, Codes and Cryptography

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Abstract

We classify all self dual and anti self dual quadratic bent functions in 2n variables under the action of the orthogonal group $${{O}(2n,\mathbb F_2)}$$ . This is done through a classification of all 2n 脳 2n involutory alternating matrices over $${\mathbb F_2}$$ under the action of the orthogonal group. The sizes of the $${{O}(2n,\mathbb F_2)}$$ -orbits of self dual and anti self dual quadratic bent functions are determined explicitly.