A characterization of binary bent functions

Carlet, Claude; Guillot, Philippe

doi:10.1109/isit.1997.613388

Cited by 11 publications

(16 citation statements)

References 4 publications

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“…Carlet [2] introduced the generalized partial spreads class (G P S) of bent functions and conjectured that any bent function belongs to G P S. This conjecture was proved in affirmative by Carlet and Guillot [3]. A similar construction which provides a unique representation of bent functions was proposed by Carlet and Guillot [4].…”

Section: Theorem 9 Let Nmentioning

confidence: 99%

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Bent and generalized bent Boolean functions

Stănică

Martinsen

Gangopadhyay

et al. 2012

Des. Codes Cryptogr.

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In this paper, we investigate the properties of generalized bent functions defined on Z n 2 with values in Z q , where q ≥ 2 is any positive integer. We characterize the class of generalized bent functions symmetric with respect to two variables, provide analogues of Maiorana-McFarland type bent functions and Dillon's functions in the generalized set up. A class of bent functions called generalized spreads is introduced and we show that it contains all Dillon type generalized bent functions and Maiorana-McFarland type generalized bent functions. Thus, unification of two different types of generalized bent functions is achieved. The crosscorrelation spectrum of generalized Dillon type bent functions is also characterized. We further characterize generalized bent Boolean functions defined on Z n 2 with values in Z 4 and Z 8 . Moreover, we propose several constructions of such generalized bent functions for both n even and n odd.

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Section: Theorem 9 Let Nmentioning

confidence: 99%

“…Taking any such bent set of cardinality ≥ 4, say 3 , which satisfy the conditions of Theorem 19(a), because S is a bent set closed under addition.…”

Section: Case (Ii)mentioning

confidence: 99%

Bent and generalized bent Boolean functions

Stănică

Martinsen

Gangopadhyay

et al. 2012

Des. Codes Cryptogr.

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“…Qu et al [41] have found, by computer enumeration, an interesting class of bent functions with 6 variables. Carlet and Guillot [19], Dobbertin [25], Kumar et al [29], and Langevin [42] have analyzed some bent function constructions, characterizations, properties, and generalizations. Tokareva [34] introduces lower bound on the number of bent functions that can be obtained by the iterative constructions proposed by Canteaut and Charpin [43].…”

Section: Introductionmentioning

confidence: 99%

A Construction of Bent Functions of n+2 Variables from a Bent Function of n Variables and Its Cyclic Shifts

Climent

García

Requena

2014

Algebra

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We present a method to iteratively construct new bent functions of + 2 variables from a bent function of variables and its cyclic shift permutations using minterms of variables and minterms of 2 variables. In addition, we provide the number of bent functions of + 2 variables that we can obtain by applying the method here presented, and finally we compare this method with a previous one introduced by us in 2008 and with the Rothaus and Maiorana-McFarland constructions.

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“…From the preceding discussion, such a word satisfies We note that Wada [30] has also recently recognised the connection between bent functions and PAPR reduction in MC-CDMA. Bent functions have received a good deal of attention, see for example [1], [4], [5], [8], [28], [29], [33], and a brief overview can be found in [17, Chap. 14, Sec.…”

Section: A Walsh-hadamard Transforms and Bent Functionsmentioning

confidence: 99%

On codes with low peak-to-average power ratio for multi-code CDMA

Paterson¹

Proceedings IEEE International Symposium on Information Theory,

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Codes which reduce the peak-to-average power (PAPR) in multi-code code division multiple access (MC-CDMA) communications systems are systematically studied. The problem of designing such codes is reformulated as a new coding-theoretic problem: codes with low PAPR are ones in which the codewords are far from the first-order ReedMuller code. Bounds on the trade-off between rate, PAPR and error-correcting capability of codes for MC-CDMA follow. The connections between the code design problem, bent functions and algebraic coding theory (in particular, the Kerdock codes and Delsarte-Goethals codes) are exploited to construct code families with flexible parameters for the small values of n of practical interest. In view of their algebraic structure, these codes enjoy efficient encoding and decoding algorithms. The paper concludes by listing open problems in algebraic coding theory and Boolean functions motivated by the paper.

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A characterization of binary bent functions

Abstract: A recent paper by Carlet introduces a general class of binary bent functions on (GF(2)) n (n even) whose elements are expressed by means of characteristic functions (indicators) of (nÂ2)-dimensional vector-subspaces of (GF(2))

Cited by 11 publications

References 4 publications

Bent and generalized bent Boolean functions

Bent and generalized bent Boolean functions

A Construction of Bent Functions of n+2 Variables from a Bent Function of n Variables and Its Cyclic Shifts

On codes with low peak-to-average power ratio for multi-code CDMA

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