The Internet Archive has a preservation copy of this work in our general collections.
The file type is application/pdf.
Filters
p-ary sequences with six-valued cross-correlation function: a new decimation of Niho type
[article]
2011
arXiv
pre-print
Preserved Fulltext
Using generalized Niho's Theorem, we show that the cross-correlation function between a p-ary m-sequence of period p^n-1 and its decimated sequence by the above d is at most six-valued and we can easily ...
For an odd prime p and n=2m, a new decimation d=(p^m-1)^2/2+1 of Niho type of m-sequences is presented. ...
Conclusion In this note, using generalized Niho's Theorem, we give an alternative proof of a known result. ...
arXiv:1105.2783v1
fatcat:nztrqqvhzzckbmzvshesk2pmwe
Binary m-sequences with three-valued crosscorrelation: a proof of Welch's conjecture
2000
IEEE Transactions on Information Theory
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2011; you can also visit the original URL.
The file type is application/pdf.
a binary maximum-length linear shift register sequences of degree and a decimation of that sequence by 2 + 3 takes on precisely the three values 1 1 2 +1 . ...
We prove the long-standing conjecture of Welch stating that for odd = 2 + 1, the power function with = 2 + 3 is maximally nonlinear on GF (2 ) or, in other terms, that the crosscorrelation function between ...
They would also like to thank the members of the Research Group ESAT-COSIC, especially Prof. B. Preneel, for their hospitality. ...
doi:10.1109/18.817504
fatcat:rfu6sfax65f4ve22iszb2rhyd4
Construction of bent functions via Niho power functions
2006
Journal of combinatorial theory. Series A
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is application/pdf.
A Boolean function with an even number n = 2k of variables is called bent if it is maximally nonlinear. We present here a new construction of bent functions. ...
We prove for several pairs of (d 1 , d 2 ) that f is a bent function, when 1 and 2 fulfill certain conditions. ...
Niho's theorem and Dickson polynomials Niho's theorem [9] is presented below. For the reader's convenience, we include a proof (cf. [5] ).
Theorem 10. ...
doi:10.1016/j.jcta.2005.07.009
fatcat:nvur3trxizgfxc6mxi4miohvjy
A New Characterization of Almost Bent Functions
[chapter]
1999
Lecture Notes in Computer Science
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2006; you can also visit the original URL.
The file type is application/pdf.
We here give a necessary and sufficient condition for an almost perfect nonlinear function to be almost bent. ...
This notably enables us to exhibit some infinite families of power functions which are not almost bent. L. Knudsen (Ed.): FSE'99 ...
Since R n is a principal domain, any cyclic code C of length n is generated by a unique monic polynomial g having minimal degree. ...
doi:10.1007/3-540-48519-8_14
fatcat:7bj4pa3gcnbixpb3ykrjccwuda
Page 4595 of Mathematical Reviews Vol. , Issue 2002F
[page]
2002
Mathematical Reviews
Preserved Fulltext
The Internet Archive has digitized a microfilm copy of this work. It may be possible to borrow a copy for reading.
Pless power moment identities and a theorem concerning cyclic codes due to McEliece are used to reduce the conjectures to theorems due to Dobbertin concerning certain almost perfect nonlinear mappings. ...
In this note we generalize this to |1 + Cy(t)| < cel /pr for p > 3. ...
The resolution of Niho's last conjecture concerning sequences, codes, and Boolean functions
[article]
2021
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2021; you can also visit the original URL.
The file type is application/pdf.
Other Versions
A new method is used to resolve a long-standing conjecture of Niho concerning the crosscorrelation spectrum of a pair of maximum length linear recursive sequences of length 2^2 m-1 with relative decimation ...
The method used to obtain this result proves constraints on the number of roots that certain seventh degree polynomials can have on the unit circle of a finite field. ...
A generalization of Niho's result was stated in [Ros06, Theorem 2]; we now state and prove a corrected 3 version. Lemma 2.5. ...
arXiv:2006.12239v4
fatcat:ibji7h2nmva33dqbrsy2u44jbq
On the Weight Distribution of Cyclic Codes with Niho Exponents
[article]
2014
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf.
More specifically, we obtain two classes of binary three-weight and four-weight cyclic codes and a class of nonbinary four-weight cyclic codes. ...
Recently, there has been intensive research on the weight distributions of cyclic codes. In this paper, we compute the weight distributions of three classes of cyclic codes with Niho exponents. ...
In the second part, we introduce Delsarte's Theorem and Niho's Theorem. A generalization of Niho's Theorem over odd characteristic is also presented. ...
arXiv:1401.1887v1
fatcat:hl26xuvb2zgijjx6ugkbjga4o4
Weight Divisibility of Cyclic Codes, Highly Nonlinear Functions on F2m, and Crosscorrelation of Maximum-Length Sequences
2000
SIAM Journal on Discrete Mathematics
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2006; you can also visit the original URL.
The file type is application/pdf.
Using McEliece's theorem we give some general results on the weight divisibility of duals of cyclic codes with two zeros; specifically, we exhibit some infinite families of pairs of maximum-length sequences ...
Primitive cyclic codes with two zeros whose dual satisfies this property actually correspond to almost bent power functions and to pairs of maximum-length sequences with preferred crosscorrelation. ...
This general condition generalizes the Sarwate-Pursley conjecture [31, 25] on the nonexistence of preferred pairs of m-sequences of length (2 m −1) when 4 divides m. Theorem 7.1. ...
doi:10.1137/s0895480198350057
fatcat:btcaxk4azbfz3cvmdjnx2rewvu
New pairs of m-sequences with 4-level cross-correlation
2005
Finite Fields and Their Applications
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is application/pdf.
Let be a primitive element of GF (2 n ), where n ≡ 0(mod 4). Let d = (2 2k + 2 s+1 − 2 k+1 − 1)/(2 s −1), where n=2k, and s is such that 2s divides k. ...
We prove that the binary m-sequences s(t) = tr( t ) and s(dt) have a four-level cross-correlation function and give the distribution of the values. ...
A central problem in the theory of m-sequences, and in sequence design in general, is to determine the values and the number of occurrences of each value taken on by the cross-correlation function C d ...
doi:10.1016/j.ffa.2004.09.001
fatcat:gi3nkrf4jbceloafh3ftx76td4
On Niho type cross-correlation functions of m-sequences
2007
Finite Fields and Their Applications
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is application/pdf.
In addition, we give a simple proof of the fact that the cross-correlation function between two m-sequences, which differ by a decimation of this type, is at least four-valued. ...
We study the number of solutions to (x + 1) d = x d + 1 in GF(q 2 ). ...
Secondly, a family containing both of Niho's families was found in [9] . Niho's theorem in turn was generalized to nonbinary sequences in [14] . ...
doi:10.1016/j.ffa.2005.09.004
fatcat:myeujn35tja4hc5dnhicgapyhy
On Inversion in Z_2^n-1
[article]
2013
arXiv
pre-print
Preserved Fulltext
The Internet Archive has a preservation copy of this work in our general collections.
The file type is application/pdf.
Other Versions
We studied the function (n), which for a fixed positive integer d maps integers n≥ 1 to the least positive residue of the inverse of d modulo 2^n-1, if it exists. ...
In this paper we determined explicitly the multiplicative inverses of the Dobbertin and Welch APN exponents in Z_2^n-1, and we described the binary weights of the inverses of the Gold and Kasami exponents ...
For a generic integer d we cannot of course expect to be able to guess its inverse modulo 2 n − 1. ...
arXiv:1303.0716v2
fatcat:wnumwi7jdbhqnfnrlygzwx3lai
The only crooked power functions are x2k+2l
2007
European journal of combinatorics (Print)
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is application/pdf.
} is the complement of a hyperplane for every fixed a ∈ F * 2 n (where F 2 n is considered as a vector space over F 2 ). ...
Our proof is an easy generalization of the proof given in [10] . Given α ∈ F * 2 n , we define b α : F 2 n → F 2 by b α (β) = 1 if W f (α, β) = 0 0 otherwise. Lemma 2. ...
Lemma 2 and Theorem 2 imply the following statement. Theorem 2 ([ |F α ∩ H i (β 1 ) ∩ H j (β 2 )| ∈ {2 n−3 , 2 n−3 ± 2 n−3 2 }, for all α, β 1 = β 2 ∈ F * 2 n and i, j ∈ F 2 . ...
doi:10.1016/j.ejc.2006.01.010
fatcat:l63qw3rsi5bfnopblbzgkkym5u
On the Correlation Distribution for a Ternary Niho Decimation
[article]
2016
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is application/pdf.
By studying the weight distribution of the ternary Zetterberg code and counting the numbers of solutions of some equations over the finite field F_3^n, the correlation distribution between a ternary m-sequence ...
This is the first time that the correlation distribution for a non-binary Niho decimation has been determined since 1976. ...
The possible values of S(a, b) given in Lemma 7 below can be found by the techniques used in Lemma 2 of [18] , which originate from the proof of Niho's Theorem [21] . ...
arXiv:1612.06686v1
fatcat:7s7uaqmdunhmvbz2uiqzwdizqe
Crooked maps in F2n
2007
Finite Fields and Their Applications
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is application/pdf.
This is a generalization of a result in [17] . There are some indications that the complete characterization of crooked maps is difficult. ...
In Section 2 we generalize the notion of crooked maps and give some properties of such maps. ...
A special case of Lemma 2 with p = 2, odd n and δ = γ = 1 was proved in [13, 18] . The statement of Corollary 6 can be generalized for the following class of maps. Proof. ...
doi:10.1016/j.ffa.2006.03.003
fatcat:mhhj2x6nhng5rc4fdsxgegytqy
Improved Lower Bounds for the Fourier Entropy/Influence Conjecture via Lexicographic Functions
[article]
2017
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf.
Additionally, we prove a Lipschitz-type condition on the total influence and spectral entropy, which may be of independent interest. ...
The Fourier Entropy/Influence conjecture of Friedgut and Kalai from 1996 states that the entropy to influence ratio is bounded by a universal constant C. ...
Generalizing the composition method Here is a sketch of the proof of Proposition 1.2, as done in [9, Lemma 5.1]. ...
arXiv:1711.00762v1
fatcat:rvmk5svaxregpe4sd2bv2kcxcy
« Previous
Showing results 1 — 15 out of 20 results