Nonbinary Kasami sequences over GF(p)

Liu, S.-C.; Komo, J.J.

doi:10.1109/18.144728

Cited by 53 publications

(15 citation statements)

References 5 publications

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“…These identities completely agree with (2). ⊓ ⊔ Corollary 4 (p-ary Kasami [5]) Let n = 2k and a ∈ GF(p n ) for an odd prime p. Then the function f (x) = Tr n ax p k +1 is a weakly regular bent function if…”

Section: Now Prove That Conditionmentioning

confidence: 99%

“…The value of d is given by Lemma 4. For those values of j giving d = 2 we use [4,Theorems 5.15,5.33] and the remaining cases when v(j) < v(n) are settled by [11,Lemma 3.5] (see also [13] for the proofs).…”

Section: It Is Well Known That V(pmentioning

confidence: 99%

“…These are Sidelnikov, Kumar-Moreno [3], Kasami [5], Kim et alia [6] and Coulter-Matthews [7] bent functions. Note that all these functions, except Coulter-Matthews case, are quadratic.…”

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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Section: Now Prove That Conditionmentioning

confidence: 99%

Section: It Is Well Known That V(pmentioning

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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show abstract

“…Theorem 3: For a fixed integer ρ, the minimum and Table 1 Linear span distribution of U o (ρ)(or U e (ρ)) Linear span Number of sequences n(n−2ρ+3)/2 (p n -1)/2 n(n−2ρ+5)/2 (p n -1) 2 /2 n(n−2ρ+7)/2 (p n -1) 3 /2 # # n(n+3)/2 (p n -1) ρ+1 /2 [3] (2m+1)k p n ( n,2n) 1+p n/2 Liu and komo [4] even, 2m p m ( n, 3m) 1+p n/2 Moriuchi and Imamura [5] 2m p m (3n, 3n) 1+p n/2 Helleseth [2] (2m+1)e 1+p n ( n, 2n) 1+p (n+e)/2 Jang et al [7] (2m+1)e p n ( n, (m+2)n) 1+p n/2…”

Section: The Linear Span Of U O (ρ) and U E (ρ)mentioning

confidence: 99%

“…To resist attacks from the application of the Berlekamp-Massey algorithm, the sequences should also have large linear span. Hence, such sequences are widely investigated and many families with low correlation are presented [4,5,7,8,9,10,11,12] .…”

Section: Introductionmentioning

confidence: 99%