New results on quasi-subfield polynomials

Euler, Marie; Petit, Christophe

doi:10.1016/j.ffa.2021.101881

Search citation statements

Order By: Relevance

Paper Sections

Select...

A New Family Of σ-Linearized Trinomials With Maximum Kernel1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2022

Publication Types

Select...

Other1

Article1

Relationship

Self Cite0

Independent2

Authors

Journals

Cited by 2 publications

(1 citation statement)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Hence, System (31) is equivalent to 12 , N q 15 /q (a) = N q 15 /q (b) = −1, that is N q 15 /q 3 (b), N q 15 /q 3 (b) σ , N q 15 /q 3 (b) σ 2 are distinct solutions of…”

Section: A New Family Of σ-Linearized Trinomials With Maximum Kernelmentioning

confidence: 99%

Linearized trinomials with maximum kernel

Santonastaso¹,

Zullo²

2020

Preprint

View full text Add to dashboard Cite

Linearized polynomials have attracted a lot of attention because of their applications in both geometric and algebraic areas. Let q be a prime power, n be a positive integer and σ be a generator of Gal(F q n : F q ). In this paper we provide closed formulas for the coefficients of a σ-trinomial f over F q n which ensure that the dimension of the kernel of f equals its σ-degree, that is linearized polynomials with maximum kernel. As a consequence, we present explicit examples of linearized trinomials with maximum kernel and characterize those having σ-degree 3 and 4. Our techniques rely on the tools developed in [22]. Finally, we apply these results to investigate a class of rank metric codes introduced in [8], to construct quasi subfield polynomials and cyclic subspace codes, obtaining new solutions to the conjecture posed in [35].

show abstract

“…Hence, System (31) is equivalent to 12 , N q 15 /q (a) = N q 15 /q (b) = −1, that is N q 15 /q 3 (b), N q 15 /q 3 (b) σ , N q 15 /q 3 (b) σ 2 are distinct solutions of…”

Section: A New Family Of σ-Linearized Trinomials With Maximum Kernelmentioning

confidence: 99%