Prime-phase sequences with periodic correlation properties better than binary sequences

Kumar, P. Vijay; Moreno, Oscar

doi:10.1109/18.79916

Cited by 155 publications

(55 citation statements)

References 13 publications

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“…The existence of a solution in (4) The above proposition generalises the result obtained by Kumar and Moreno in the Section II of [10]. As there, it could be possible to give a complete description of the Fourier coefficient distribution by means of quadratic Gauss sums.…”

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confidence: 49%

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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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confidence: 49%

“…If we apply Theorem 5.1 in the case of q-degree equal to 2, we recovered the theorem given Kumar and Moreno [10], but this is also a consequence of Proposition 3.1. In particular, the bound is optimal.…”

Section: Numerical Results and Final Remarksmentioning

confidence: 57%

ESTIMATION OF SOME EXPONENTIAL SUM BY MEANS OF q-DEGREE

Gillot¹,

Langevin²

2010

Glasgow Math. J.

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“…Corollary 5 (Kumar, Moreno [3]) Let n = ek for an odd integer k and integer r in the range 1 ≤ r ≤ k with gcd(r, k) = 1. Then the function f (x) = Tr n ax…”

Section: Now Prove That Conditionmentioning

confidence: 99%

“…Thus, regular bent functions can only be found for even n and for odd n with p ≡ 1 (mod 4). Here we note a minor inaccuracy found in [3,Theorem 9] that contains a statement equivalent to (2). In the correct version e there should be replaced with n and ± ω k should also stand for the case of even n.…”

Section: Introductionmentioning

confidence: 99%

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Monomial and quadratic bent functions over the finite fields of odd characteristic

Helleseth

Kholosha

2006

IEEE Trans. Inform. Theory

192

186

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We consider p-ary bent functions of the form f (x) = TrnA new class of ternary monomial regular bent function with the Dillon exponent is discovered. The existence of Dillon bent functions in the general case is an open problem of deciding whether a certain Kloosterman sum can take on the value −1. Also described is the general Gold-like form of a bent function that covers all the previously known monomial quadratic cases. We also discuss the (weak) regularity of our new as well as of known monomial bent functions and give the first example of a not weakly regular bent function. Finally we prove some criteria for an arbitrary quadratic functions to be bent.

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Ternary Sequences

Helleseth¹

2003

Wiley Encyclopedia of Telecommunications

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Methods for constructing ternary sequences with good auto‐ and crosscorrelation properties are described. Focus is on designing families of sequences with good parameters for Code‐Division‐Multiple‐Access(CDMA) applications. Techniques for constructing good ternary sequence designs are presented using basic ideas from Galois fields, the trace function and properties of the auto‐ and crosscorrelation of m ‐sequences. Bounds on the possible parameters of the best families of sequences are presented as well as several constructions of asymptotically optimal ternary sequences. These sequence families have better parameters than possible for comparable binary designs.

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Prime-phase sequences with periodic correlation properties better than binary sequences

Cited by 155 publications

References 13 publications

ESTIMATION OF SOME EXPONENTIAL SUM BY MEANS OF q-DEGREE

ESTIMATION OF SOME EXPONENTIAL SUM BY MEANS OF q-DEGREE

Monomial and quadratic bent functions over the finite fields of odd characteristic

Ternary Sequences

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