Abstract
One of the hardest problems in coding theory is to evaluate the covering radius of first order Reed–Muller codes RM(1,m), and more recently the balanced covering radius for crypto graphical purposes. The aim of this paper is to present some new results on this subject. We mainly study boolean functions invariant under the action of some finite groups, following the idea of Patterson and Wiedemann [The covering radius of the (1, 15) Reed-Muller Code is atleast 16276. IEEE Trans Inform Theory. Vol. 29 (1983) 354.]. Our method is Fourier transforms and our results are both theoretical and numerical.
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Langevin, P., Zanotti, JP. Nonlinearity of Some Invariant Boolean Functions. Des Codes Crypt 36, 131–146 (2005). https://doi.org/10.1007/s10623-004-1700-x
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DOI: https://doi.org/10.1007/s10623-004-1700-x