scholarly journals MRD-codes and linear sets

2017 ◽  
Vol 149 ◽  
pp. 1-20 ◽  
Author(s):  
Guglielmo Lunardon
Keyword(s):  
Linear Sets ◽  
Mrd Codes

scholarly journals Maximum scattered linear sets and MRD-codes

2017 ◽  
Vol 46 (3-4) ◽  
pp. 517-531 ◽  
Author(s):  
Bence Csajbók ◽  
Giuseppe Marino ◽  
Olga Polverino ◽  
Ferdinando Zullo
Keyword(s):  
Linear Sets ◽  
Mrd Codes

scholarly journals Linear sets and MRD-codes arising from a class of scattered linearized polynomials

2021 ◽  
Author(s):  
Giovanni Longobardi ◽  
Corrado Zanella
Keyword(s):  
Minimum Distance ◽  
Infinite Family ◽  
Discrete Math ◽  
Projective Line ◽  
Linear Automorphism ◽  
Linear Sets ◽  
Field Extensions ◽  
Linearized Polynomials ◽  
Mrd Codes

AbstractA class of scattered linearized polynomials covering infinitely many field extensions is exhibited. More precisely, the q-polynomial over $${{\mathbb {F}}}_{q^6}$$ F q 6 , $$q \equiv 1\pmod 4$$ q ≡ 1 ( mod 4 ) described in Bartoli et al. (ARS Math Contemp 19:125–145, 2020) and Zanella and Zullo (Discrete Math 343:111800, 2020) is generalized for any even $$n\ge 6$$ n ≥ 6 to an $${{{\mathbb {F}}}_q}$$ F q -linear automorphism $$\psi (x)$$ ψ ( x ) of $${{\mathbb {F}}}_{q^n}$$ F q n of order n. Such $$\psi (x)$$ ψ ( x ) and some functional powers of it are proved to be scattered. In particular, this provides new maximum scattered linear sets of the projective line $${{\,\mathrm{{PG}}\,}}(1,q^n)$$ PG ( 1 , q n ) for $$n=8,10$$ n = 8 , 10 . The polynomials described in this paper lead to a new infinite family of MRD-codes in $${{\mathbb {F}}}_q^{n\times n}$$ F q n × n with minimum distance $$n-1$$ n - 1 for any odd q if $$n\equiv 0\pmod 4$$ n ≡ 0 ( mod 4 ) and any $$q\equiv 1\pmod 4$$ q ≡ 1 ( mod 4 ) if $$n\equiv 2\pmod 4$$ n ≡ 2 ( mod 4 ) .

scholarly journals Classes and equivalence of linear sets in PG(1,q)

2018 ◽  
Vol 157 ◽  
pp. 402-426 ◽  
Author(s):  
Bence Csajbók ◽  
Giuseppe Marino ◽  
Olga Polverino
Keyword(s):  
Linear Sets

scholarly journals G-linear sets and torsion points in definably compact groups

2009 ◽  
Vol 48 (5) ◽  
pp. 387-402 ◽  
Author(s):  
Margarita Otero ◽  
Ya’acov Peterzil
Keyword(s):  
Compact Groups ◽  
Torsion Points ◽  
Linear Sets

scholarly journals On self-dual MRD codes

2016 ◽  
Vol 10 (3) ◽  
pp. 633-642 ◽  
Author(s):  
Gabriele Nebe ◽  
Wolfgang Willems
Keyword(s):  
Mrd Codes

On the sparseness of certain linear MRD codes

2020 ◽  
Vol 596 ◽  
pp. 145-168
Author(s):  
Heide Gluesing-Luerssen
Keyword(s):  
Mrd Codes
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