On a conjecture about maximum scattered subspaces of Fq6×Fq6

Daniele Bartoli; Bence Csajbók; Maria Montanucci

doi:10.1016/j.laa.2021.08.023

On a conjecture about maximum scattered subspaces of F_q6×F_q6

Daniele Bartoli^*, Bence Csajbók, Maria Montanucci

^*Corresponding author for this work

Research output: Contribution to journal › Journal article › Research › peer-review

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Abstract

We prove that under the action of GL(2,q⁶) there are ⌊(q²+q+1)(q−2)/2⌋ equivalence classes of maximum scattered subspaces of the form U_b={(x,bx^q+x^q4):x∈F_q6} in F_q6×F_q6. This verifies a conjecture of Csajbók, Marino, Polverino and Zanella from 2018.

Original language	English
Journal	Linear Algebra and Its Applications
Volume	631
Pages (from-to)	111-135
ISSN	0024-3795
DOIs	https://doi.org/10.1016/j.laa.2021.08.023
Publication status	Published - 2021

Keywords

Scattered subspaces
Linear sets
MRD-codes

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abstract = "We prove that under the action of GL(2,q6) there are ⌊(q2+q+1)(q−2)/2⌋ equivalence classes of maximum scattered subspaces of the form Ub={(x,bxq+xq4):x∈Fq6} in Fq6×Fq6. This verifies a conjecture of Csajb{\'o}k, Marino, Polverino and Zanella from 2018.",

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AU - Bartoli, Daniele

AU - Csajbók, Bence

AU - Montanucci, Maria

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N2 - We prove that under the action of GL(2,q6) there are ⌊(q2+q+1)(q−2)/2⌋ equivalence classes of maximum scattered subspaces of the form Ub={(x,bxq+xq4):x∈Fq6} in Fq6×Fq6. This verifies a conjecture of Csajbók, Marino, Polverino and Zanella from 2018.

AB - We prove that under the action of GL(2,q6) there are ⌊(q2+q+1)(q−2)/2⌋ equivalence classes of maximum scattered subspaces of the form Ub={(x,bxq+xq4):x∈Fq6} in Fq6×Fq6. This verifies a conjecture of Csajbók, Marino, Polverino and Zanella from 2018.

KW - Scattered subspaces

KW - Linear sets

KW - MRD-codes

U2 - 10.1016/j.laa.2021.08.023

DO - 10.1016/j.laa.2021.08.023

M3 - Journal article

SN - 0024-3795

VL - 631

SP - 111

EP - 135

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

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