Generalized bent functions and their properties

Kumar, P. V. ; Scholtz, R. A. ; Welch, L. R. (1985) Generalized bent functions and their properties Journal of Combinatorial Theory, Series A, 40 (1). pp. 90-107. ISSN 0097-3165

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Jet Jqm denote the set of m-tuples over the integers modulo q and set i = -1, w = ei(2πq). As an extension of Rothaus' notion of a bent function, a function f, f: Jqm → Jq1 is called bent if all the Fourier coefficients of wf have unit magnitude. An important feature of these functions is that their out-of-phase autocorrelation value is identically zero. The nature of the Fourier coefficients of a bent function is examined and a proof for the non-existence of bent functions over Jqm, m odd, is given for many values of q of the form q = 2 (mod 4). For every possible value of q and m (other than m odd and q = 2 (mod 4)), constructions of bent functions are provided.

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ID Code:110295
Deposited On:31 Jan 2018 10:42
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