Generalized bent functions and their properties

Kumar, Pradeep; Scholtz, R.A.; Welch, L. R.

doi:10.1016/0097-3165(85)90049-4

Cited by 382 publications

(239 citation statements)

References 6 publications

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“…Olsen et al [4] constructed a family of binary sequences with optimal correlation based on binary bent functions. Kumar et al [11] generalized binary bent functions to p-ary bent functions and they [5] used these functions to construct p-ary bent sequences. In this paper, we propose a new concept named similar-bent function, the maximum absolute value of whose walsh spectrum is small.…”

Section: Introductionmentioning

confidence: 99%

New constructions of low-correlation sequences with high-linear complexity

Xiong¹,

Li²,

Dai³

et al. 2012

IET Commun.

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Abstract. In this paper, we propose a new concept named similar-bent function and we present two general methods to construct balanced sequences with low correlation by using similar-bent functions and orthogonal similar-bent functions. We find that the bent sequence sets are special cases of our construction. We also investigate the linear complexity of the new constructed sequences. If a suitable similar-bent function is given, the sequences constructed by it can have high linear complexity. As examples, we construct two new low correlation sequence sets. One constructed based on Dobbertin's iterative function is asymptotically optimal with respect to Welch's bound and the other one is constructed based on Kasami function whose sequences have a high linear complexity.

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Section: Introductionmentioning

confidence: 99%

New constructions of low-correlation sequences with high-linear complexity

Xiong¹,

Li²,

Dai³

et al. 2012

IET Commun.

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“…Bent functions were first introduced by Rothaus [16] in 1976, and were generalized to GBFs by Kumar et al [9] in 1985. GBFs have been used in many fields such as difference sets, coding theory, cryptography and sequence designs.…”

Section: Introductionmentioning

confidence: 99%

“…GBFs have been used in many fields such as difference sets, coding theory, cryptography and sequence designs. For more background information and its applications we refer the reader to [2,14,9].…”

Section: Introductionmentioning

confidence: 99%

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On the Non-Existence of Certain Classes of Generalized Bent Functions

Lv¹,

Li²

2017

IEEE Trans. Inform. Theory

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“…There exists polynomials of spectral amplitude √ q m , they define generalised bent functions, see for example [11]. For remark that only a very small number of bent functions of monomial form are known, see [7].…”

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confidence: 99%

ESTIMATION OF SOME EXPONENTIAL SUM BY MEANS OF q-DEGREE

Gillot¹,

Langevin²

2010

Glasgow Math. J.

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Abstract. In this paper, we improve results of Gillot, Kumar and Moreno to estimate some exponential sums by means of q-degrees. The method consists in applying suitable elementary transformations to see an exponential sum over a finite field as an exponential sum over a product of subfields in order to apply Deligne bound. In particular, we obtain new results on the spectral amplitude of some monomials. Introduction.Exponential sums and bounds for them are exploited by coding theorists and communications engineers [15]. The minimal distance of dual BCH and other cyclic codes can be evaluated in terms of exponential sums. They are also useful in the study of sequences with small correlations for spread-spectrum and other communication applications. In both cases, the estimation of exponential sums is often a key point for the construction of a good code. In this paper, we focus on the estimation of exponential sums over finite fields for some polynomials. First, we begin introducing the tools and known results about spectral amplitude. Then, we generalise results of Kumar and Moreno [10] over spectral amplitude of some monomials in odd characteristics. We define the q-degree and the principle of multivariate point of view to be able to apply the results of Deligne [4] for exponential sums over a product of finite fields. Thus, we obtain a bound in terms of q-degree generalising the result of Gillot [6].

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Generalized bent functions and their properties

Cited by 382 publications

References 6 publications

New constructions of low-correlation sequences with high-linear complexity

New constructions of low-correlation sequences with high-linear complexity

On the Non-Existence of Certain Classes of Generalized Bent Functions

ESTIMATION OF SOME EXPONENTIAL SUM BY MEANS OF q-DEGREE

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