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Generalized bent functions and their properties. (English) Zbl 0585.94016
After defining ”generalized bent functions”, the authors study the nature of the Fourier coefficients of a bent function, and a proof for the non- existence of bent functions over $$J^ m_ q$$, m odd, is given for many values of q of the form $$q=2(mod 4)$$. For every value of q and m (other than m odd and $$q=2(mod 4))$$, constructions for bent functions over $$J^ m_ q$$ are provided. Some properties of generalized bent functions are also examined, and it is shown that the generalized versions share many properties, such as the connection with Hadamard matrices, in common with their binary counterparts.
Reviewer: B.K.Dass

##### MSC:
 94B99 Theory of error-correcting codes and error-detecting codes 94A99 Communication, information 05B20 Combinatorial aspects of matrices (incidence, Hadamard, etc.) 11T06 Polynomials over finite fields
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