Abstract
We define and characterise selfnegadual generalised quadratic Boolean functions by establishing a link, both to the multiplicative order of symmetric binary matrices, and also to the Hermitian self-dual \({\mathbb{F}_4}\)-linear codes. This facilitates a novel way to classify Hermitian self-dual \({\mathbb{F}_4}\)-linear codes.
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This is one of several papers published in Designs, Codes and Cryptography comprising the “Special Issue on Coding and Cryptography”.
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Danielsen, L.E., Parker, M.G. The selfnegadual properties of generalised quadratic Boolean functions. Des. Codes Cryptogr. 66, 305–316 (2013). https://doi.org/10.1007/s10623-012-9693-3
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DOI: https://doi.org/10.1007/s10623-012-9693-3
Keywords
- Generalised Boolean functions
- Selfnegadual functions
- Negabent functions
- Bent functions
- NegaHadamard transform
- Walsh–Hadamard transform
- Fourier eigenspectra
- Selfdual codes
- Quantumcodes