Cryptology ePrint Archive: Report 2012/037

Some results on $q$-ary bent functions

Deep Singh, Maheshanand Bhaintwal and Brajesh Kumar Singh

Abstract: Kumar et al.(1985) have extended the notion of classical bent Boolean functions in the generalized setup on $\BBZ_q^n$. They have provided an analogue of classical Maiorana-McFarland type bent functions. In this paper, we study the crosscorrelation of a subclass of such generalized Maiorana-McFarland (\mbox{GMMF}) type bent functions. We provide a construction of quaternary ($q = 4$) bent functions on $n+1$ variables in terms of their subfunctions on $n$-variables. Analogues of sum-of-squares indicator and absolute indicator of crosscorrelation of Boolean functions are defined in the generalized setup. Further, $q$-ary functions are studied in terms of these indictors and some upper bounds of these indicators are obtained. Finally, we provide some constructions of balanced quaternary functions with high nonlinearity under Lee metric.

Category / Keywords: $q$-ary bent functions; Walsh-Hadamard transform; Parseval's identity; GMMF type bent functions; Crosscorrelation

Date: received 23 Jan 2012, last revised 22 Apr 2012

Contact author: deepsinghspn at gmail com

Available format(s): PDF | BibTeX Citation

Note: Dear Sir, We have included section 4, as a new section and updated section other results in the same section. Also, we have updated abstract as well as introduction accordingly.

Version: 20120422:164807 (All versions of this report)

Short URL: ia.cr/2012/037

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