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Exceptional scattered polynomials (Q1643204)

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Language	Label	Description	Also known as
English	Exceptional scattered polynomials	scientific article

Statements

scholarly article

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Exceptional scattered polynomials (English)

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Daniele Bartoli

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Journal of Algebra

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publication date

18 June 2018

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full work available at URL

https://arxiv.org/abs/1708.00349

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zbMATH Keywords

maximum scattered linear set

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MRD code

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algebraic curve

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finite field

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Hasse-Weil bound

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MaRDI profile type

MaRDI publication profile

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Linear \((q+1)\)-fold blocking sets in \(\text{PG} (2,q^4)\)

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Scattered spaces with respect to a spread in \(\text{PG}(n,q)\)

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On two-intersection sets with respect to hyperplanes in projective spaces

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Semifield planes of order \(q^4\) with kernel \(\mathbb F_{q^2}\) and center \(\mathbb F_q\)

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A new large class of functions not APN infinitely often

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On the classification of hyperovals

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Exceptional planar polynomials

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Non-linear maximum rank distance codes

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Maximum scattered linear sets and MRD-codes

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On the equivalence of linear sets

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Bilinear forms over a finite field, with applications to coding theory

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Non-linear maximum rank distance codes in the cyclic model for the field reduction of finite geometries

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Hyperovals in Knuth's binary semifield planes

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Infinite families of new semifields

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Theory of codes with maximum rank distance

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Galois theory and linear algebra

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Proof of a conjecture of Segre and Bartocci on monomial hyperovals in projective planes

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Proof of a conjecture on the sequence of exceptional numbers, classifying cyclic codes and APN functions

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New criteria for MRD and Gabidulin codes and some rank-metric code constructions

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Double-error-correcting cyclic codes and absolutely irreducible polynomials over \(\text{GF}(2)\)

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APN monomials over \(\mathrm{GF}(2^n)\) for infinitely many \(n\)

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Coding for Errors and Erasures in Random Network Coding

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Scattered spaces in Galois geometry

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Field reduction and linear sets in finite geometry

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Functions which are PN on infinitely many extensions of \(\mathbb F_p\), \(p\) odd

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Linear \(k\)-blocking sets

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Maximum scattered linear sets of pseudoregulus type and the Segre variety \(\mathcal{S}_{n,n}\)

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Blocking sets of size \(q^t + q^{t-1} + 1\)

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Blocking sets and derivable partial spreads

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On kernels and nuclei of rank metric codes

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Towards the classification of rank 2 semifields 6-dimensional over their center

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Equivalence for Rank-Metric and Matrix Codes and Automorphism Groups of Gabidulin Codes

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Additive Rank Metric Codes

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Linear sets in finite projective spaces

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Functions of degree \(4e\) that are not APN infinitely often

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Planar functions over fields of characteristic two

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A new family of linear maximum rank distance codes

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Planar functions and perfect nonlinear monomials over finite fields

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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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10.1016/J.JALGEBRA.2018.03.010

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Sitelinks

Mathematics(1 entry)

mardi Publication:1643204

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