On Boolean functions with the sum of every two of them being bent

Bey, Christian; Kyureghyan, Gohar M.

doi:10.1007/s10623-008-9196-4

Cited by 18 publications

(19 citation statements)

References 10 publications

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“…Let ζ = e 2πı/q be the q-primitive root of unity, and f : Z n 2 → Z q as in (1). It turns out that the generalized Walsh-Hadamard spectrum of f can be described (albeit, in a complicated manner) in terms of the Walsh-Hadamard spectrum of its Boolean components a i .…”

Section: Then F Is a Gbent Function If And Only Ifmentioning

confidence: 99%

Bent and Generalized Bent Boolean Functions

Stănică¹,

Martinsen²,

Gangopadhyay³

et al. 2012

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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: Then F Is a Gbent Function If And Only Ifmentioning

confidence: 99%

Bent and Generalized Bent Boolean Functions

Stănică¹,

Martinsen²,

Gangopadhyay³

et al. 2012

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show abstract

“…Recall that the parameters of a difference set in a group of order 2 d 2 +2 are determined by Theorem 1.2 and can be regarded as McFarland parameters with q = 2, and that when q is prime we do not need to specify an isomorphism ϕ in Theorem 4.2. be the subgroups of G corresponding to the hyperplanes of E when E is regarded as a vector space of dimension d + 1 over GF (2). Then, the sets…”

Section: Main Construction Theoremmentioning

confidence: 99%

“…Firstly, the expression now has index q in E (where E is isomorphic to the elementary abelian group of order q d+1 ). G contains a reduced linking system of difference sets of size m − 1.be the subgroups of G corresponding to the hyperplanes of E when E is regarded as a vector space of dimension d + 1 over GF(2).…”

mentioning

confidence: 99%

“… , and , and the result follows from Theorem 5.6. be the subgroups of G corresponding to hyperplanes of E when E is regarded as a vector space of dimension d + 1 over GF (2). We may take…”

mentioning

confidence: 99%

“…3 . (We cannot directly compare this count of reduced linking systems of difference sets with the classification of systems of linked symmetric (16,6,2,4) designs given by Mathon [22], which counts the number of isomorphism classes rather than the number of distinct systems. )…”

mentioning

confidence: 99%

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Linking systems of difference sets

Jedwab

Simon

2018

J of Combinatorial Designs

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A linking system of difference sets is a collection of mutually related group difference sets, whose advantageous properties have been used to extend classical constructions of systems of linked symmetric designs. The central problems are to determine which groups contain a linking system of difference sets, and how large such a system can be. All previous constructive results for linking systems of difference sets are restricted to 2‐groups. We use an elementary projection argument to show that neither the McFarland/Dillon nor the Spence construction of difference sets can give rise to a linking system of difference sets in non‐2‐groups. We make a connection to Kerdock and bent sets, which provides large linking systems of difference sets in elementary abelian 2‐groups. We give a new construction for linking systems of difference sets in 2‐groups, taking advantage of a previously unrecognized connection with group difference matrices. This construction simplifies and extends prior results, producing larger linking systems than before in certain 2‐groups, new linking systems in other 2‐groups for which no system was previously known, and the first known examples in nonabelian groups.

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Asymptotic Behavior of Perturbations of Symmetric Functions

Castro

Medina

2014

Ann. Comb.

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On Boolean functions with the sum of every two of them being bent

Cited by 18 publications

References 10 publications

Bent and Generalized Bent Boolean Functions

Bent and Generalized Bent Boolean Functions

Linking systems of difference sets

Asymptotic Behavior of Perturbations of Symmetric Functions

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