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 × 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.
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Communicated by A. Pott.
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Hou, XD. Classification of self dual quadratic bent functions. Des. Codes Cryptogr. 63, 183–198 (2012). https://doi.org/10.1007/s10623-011-9544-7
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DOI: https://doi.org/10.1007/s10623-011-9544-7
Keywords
- Alternating matrix
- Bent function
- Orthogonal group
- Quadratic function
- Self dual bent function
- Symplectic group