Exceptional scattered sequences

Daniele Bartoli; Giuseppe Marino; Alessandro Neri; Lara Vicino

doi:10.5802/alco.377

Exceptional scattered sequences

Daniele Bartoli, Giuseppe Marino, Alessandro Neri, Lara Vicino

Algebra

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Abstract

The concept of scattered polynomials is generalized to those of exceptional scattered sequences which are shown to be the natural algebraic counterpart of Fqn-linear MRD codes. The first infinite family in the first nontrivial case is also provided and equivalence issues are considered. As a byproduct, a new infinite family of MRD codes is obtained.

Original language	English
Pages (from-to)	1405-1431
Number of pages	27
Journal	Algebraic Combinatorics
Volume	7
Issue number	5
DOIs	https://doi.org/10.5802/alco.377
Publication status	Published - 2024

Keywords

finite fields
linearized polynomials
MRD codes
Scattered polynomials

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10.5802/alco.377Licence: CC BY

Exceptional scattered sequences Final publisher's version, 1.05 MBLicence: CC BY

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title = "Exceptional scattered sequences",

abstract = "The concept of scattered polynomials is generalized to those of exceptional scattered sequences which are shown to be the natural algebraic counterpart of Fqn-linear MRD codes. The first infinite family in the first nontrivial case is also provided and equivalence issues are considered. As a byproduct, a new infinite family of MRD codes is obtained.",

keywords = "finite fields, linearized polynomials, MRD codes, Scattered polynomials",

author = "Daniele Bartoli and Giuseppe Marino and Alessandro Neri and Lara Vicino",

note = "Publisher Copyright: {\textcopyright} The author(s), 2024.",

year = "2024",

doi = "10.5802/alco.377",

language = "English",

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pages = "1405--1431",

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T1 - Exceptional scattered sequences

AU - Bartoli, Daniele

AU - Marino, Giuseppe

AU - Neri, Alessandro

AU - Vicino, Lara

N1 - Publisher Copyright: © The author(s), 2024.

PY - 2024

Y1 - 2024

N2 - The concept of scattered polynomials is generalized to those of exceptional scattered sequences which are shown to be the natural algebraic counterpart of Fqn-linear MRD codes. The first infinite family in the first nontrivial case is also provided and equivalence issues are considered. As a byproduct, a new infinite family of MRD codes is obtained.

AB - The concept of scattered polynomials is generalized to those of exceptional scattered sequences which are shown to be the natural algebraic counterpart of Fqn-linear MRD codes. The first infinite family in the first nontrivial case is also provided and equivalence issues are considered. As a byproduct, a new infinite family of MRD codes is obtained.

KW - finite fields

KW - linearized polynomials

KW - MRD codes

KW - Scattered polynomials

UR - http://www.scopus.com/inward/record.url?scp=85211481329&partnerID=8YFLogxK

U2 - 10.5802/alco.377

DO - 10.5802/alco.377

M3 - Article

AN - SCOPUS:85211481329

SN - 2589-5486

VL - 7

SP - 1405

EP - 1431

JO - Algebraic Combinatorics

JF - Algebraic Combinatorics

IS - 5

ER -

Exceptional scattered sequences

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Keywords

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