A new family of maximum scattered linear sets in PG(1, q6)

被引：21

作者：

Bartoli, Daniele ^{[1
]}

Zanella, Corrado ^{[2
]}

Zullo, Ferdinando ^{[3
]}

机构：

[1] Univ Perugia, Dipartimento Matemat & Informat, Perugia, Italy

[2] Univ Padua, Dipartimento Tecn & Gest Sistemi Ind, Vicenza, Italy

[3] Univ Campania Luigi Vanvitelli, Dipartimento Matemat & Fis, Caserta, Italy

来源：

ARS MATHEMATICA CONTEMPORANEA | 2020年 / 19卷 / 01期

关键词：

Scattered linear set; MRD-code; linearized polynomial; POLYNOMIALS; EQUIVALENCE; NUMBER; ROOTS; FIELD;

D O I：

10.26493/1855-3974.2137.7fa

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We generalize the example of linear set presented by the last two authors in "Vertex properties of maximum scattered linear sets of PG(1, q(n))" (2019) to a more general family, proving that such linear sets are maximum scattered when q is odd and, apart from a special case, they are new. This solves an open problem posed in "Vertex properties of maximum scattered linear sets of PG(1, q(n))" (2019). As a consequence of Sheekey's results in "A new family of linear maximum rank distance codes" (2016), this family yields to new MRD-codes with parameters (6, 6, q; 5).

引用

页码：125 / 145

页数：21

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