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A survey on the applications of Niho exponents (Q2632844)

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Language	Label	Description	Also known as
English	A survey on the applications of Niho exponents	scientific article

Statements

scholarly article

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A survey on the applications of Niho exponents (English)

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Cryptography and Communications

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publication date

15 May 2019

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zbMATH Keywords

Niho exponent

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$m$-sequence

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bent function

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linear code

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permutation polynomial

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describes a project that uses

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MaRDI profile type

MaRDI publication profile

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full work available at URL

https://doi.org/10.1007/s12095-018-0305-6

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On constructing permutations of finite fields

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A new class of permutation trinomials constructed from Niho exponents

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Permutation polynomials, fractional polynomials, and algebraic curves

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Permutation and complete permutation polynomials

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The weight distributions of cyclic codes with two zeros and zeta functions

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Further Results on Niho Bent Functions

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On o-Equivalence of Niho Bent Functions

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Univariate Niho Bent Functions From o-Polynomials

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Binary m-sequences with three-valued crosscorrelation: a proof of Welch's conjecture

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Codes, bent functions and permutations suitable for DES-like cryptosystems

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Linear Codes From Perfect Nonlinear Mappings and Their Secret Sharing Schemes

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On Dillon's class \(H\) of bent functions, Niho bent functions and o-polynomials

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On Semibent Boolean Functions

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The number of solutions of a special system of equations in a finite field

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Cyclic codes with few weights and Niho exponents

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Some new results on cross correlation of \(p\)-ary \(m\)-sequence and its decimated sequence

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A class of binary cyclic codes with generalized Niho exponents

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\(\alpha\)-flocks and hyperovals

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\(\alpha\)-flocks with oval herds and monomial hyperovals

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Flocks and ovals

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A unified construction of finite geometries associated with <i>q</i>-clans in characteristic <i>2</i>

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Some new three-valued crosscorrelation functions for binary m-sequences

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Recent progress on weight distributions of cyclic codes over finite fields

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Cyclic Codes from Some Monomials and Trinomials

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Linear Codes From Some 2-Designs

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A construction of binary linear codes from Boolean functions

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A Class of Two-Weight and Three-Weight Codes and Their Applications in Secret Sharing

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Optimal Ternary Cyclic Codes From Monomials

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Cyclotomic Linear Codes of Order $3$

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The Weight Distributions of the Duals of Cyclic Codes With Two Zeros

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Permutation Trinomials Over Finite Fields with Even Characteristic

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Three-weight cyclic codes and their weight distributions

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One-to-one highly nonlinear power functions on \(\mathrm{GF}(2^n)\)

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Ternary m-sequences with three-valued cross-correlation function: new decimations of Welch and Niho type

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Niho type cross-correlation functions via dickson polynomials and Kloosterman sums

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Construction of bent functions via Niho power functions

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Binary cyclic codes with two primitive nonzeros

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Maximal recursive sequences with 3-valued recursive cross-correlation functions (Corresp.)

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Searching for linear codes with large minimum distance

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Some new classes of permutation trinomials over finite fields with even characteristic

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Some results about the cross-correlation function between two maximal linear sequences

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A note on the cross-correlation function between two binary maximal length linear sequences

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New pairs of \(m\)-sequences with 4-level cross-correlation.

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On Niho type cross-correlation functions of \(m\)-sequences

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Period-Different $m$-Sequences With at Most Four-Valued Cross Correlation

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Niho Bent Functions and Subiaco Hyperovals

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A proof of the Welch and Niho conjectures on cross-correlations of binary \(m\)-sequences

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Determination of a type of permutation trinomials over finite fields

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A survey of permutation binomials and trinomials over finite fields

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Permutation polynomials over finite fields -- a survey of recent advances

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Determination of a type of permutation trinomials over finite fields. II

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Determination of a type of permutation binomials over finite fields

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A Family of $m$-Sequences With Five-Valued Cross Correlation

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Further Results on $m$-Sequences With Five-Valued Cross Correlation

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Permutation polynomials of the form <i>X</i> + <i>γ</i> Tr(<i>X<sup>k</sup></i>)

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The weight enumerators for several classes of subcodes of the 2nd order binary Reed-Muller codes

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Weil sums of binomials, three-level cross-correlation, and a conjecture of Helleseth

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Divisibility of Weil sums of binomials

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Proof of a conjectured three-valued family of Weil sums of binomials

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New open problems related to old conjectures by Helleseth

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A note regarding permutation binomials over \(\mathbb{F}_{q^2}\)

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Bent Functions With $2^r$ Niho Exponents

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On two conjectures about permutation trinomials over \(\mathbb{F}_{3^{2k}}\)

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The weight hierarchy of a family of cyclic codes with arbitrary number of nonzeroes

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Several classes of permutation trinomials from Niho exponents

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New permutation trinomials from Niho exponents over finite fields with even characteristic

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A class of binary cyclic codes with five weights

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On the Walsh Transform of a Class of Functions From Niho Exponents

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Several New Classes of Bent Functions From Dillon Exponents

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The Weight Distribution of a Class of Cyclic Codes Related to Hermitian Forms Graphs

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The Weight Distributions of Several Classes of Cyclic Codes From APN Monomials

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Optimal ternary cyclic codes with minimum distance four and five

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On the Weight Distribution of Cyclic Codes With Niho Exponents

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New classes of permutation binomials and permutation trinomials over finite fields

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Permutation polynomials of the form \(cx+\mathrm{Tr}_{q^l/ q}(x^a)\) and permutation trinomials over finite fields with even characteristic

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New permutation trinomials constructed from fractional polynomials

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Binary Sequences With Three-Valued Cross Correlations of Different Lengths

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Cyclic Codes and Sequences From Generalized Coulter–Matthews Function

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Binary linear codes with two or three weights from Niho exponents

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A note on permutation polynomials over finite fields

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Some new results on permutation polynomials over finite fields

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Permutation binomials over finite fields

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Linear codes with few weights from weakly regular bent functions based on a generic construction

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Vectorial Bent Functions From Multiple Terms Trace Functions

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Permutation polynomials and group permutation polynomials

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On Four-Valued Niho-Type Cross-Correlation Functions of $m$-Sequences

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A generalization of Niho's theorem

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On ``bent'' functions

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Cross-Correlation Distribution of $p$-ary $m$-Sequence of Period $p^{4k}-1$ and Its Decimated Sequences by $\left({{ p^{2k}+1}\over { 2}}\right)^{2}$

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Linear Codes With Two or Three Weights From Weakly Regular Bent Functions

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Several classes of complete permutation polynomials

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New permutation quadrinomials over \(\mathbb{F}_{2^{2m}}\)

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A class of new permutation trinomials

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Permutation polynomials of the form \(x^r f(x^{(q-1)/d)}\) and their group structure

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Cyclotomic Mapping Permutation Polynomials over Finite Fields

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Several classes of permutation trinomials over \(\mathbb {F}_{5^{n}}\) from Niho exponents

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Some classes of monomial complete permutation polynomials over finite fields of characteristic two

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Some classes of complete permutation polynomials over \(\mathbb F_q\)

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A Note on Cross-Correlation Distribution Between a Ternary $$m$$-Sequence and Its Decimated Sequence

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An Open Problem on the Distribution of a Niho-Type Cross-Correlation Function

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On the Correlation Distribution for a Niho Decimation

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The weight distributions of a class of cyclic codes. II

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Optimal Cyclic Codes With Generalized Niho-Type Zeros and the Weight Distribution

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Weight distribution of cyclic codes with arbitrary number of generalized Niho type zeroes

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Two classes of \(p\)-ary bent functions and linear codes with three or four weights

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Some permutation pentanomials over finite fields with even characteristic

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Classification of Bent Monomials, Constructions of Bent Multinomials and Upper Bounds on the Nonlinearity of Vectorial Functions

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The weight distribution of a class of linear codes from perfect nonlinear functions

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On some permutation polynomials over $\mathbb {F}_q$ of the form $x^r h(x^{(q-1)/d})$

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Some New Results on the Cross Correlation of <inline-formula> <tex-math notation="TeX">$m$ </tex-math></inline-formula>-Sequences

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A class of three-weight cyclic codes

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Linear codes with two or three weights from quadratic bent functions

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Identifiers

zbMATH Open document ID

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Mathematics Subject Classification ID

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zbMATH DE Number

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10.1007/S12095-018-0305-6

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Sitelinks

Mathematics(1 entry)

mardi Publication:2632844

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