Maximum scattered linear sets and MRD-codes |
| |
Authors: | " target="_blank">Bence Csajbók Giuseppe Marino Olga Polverino Ferdinando Zullo |
| |
Institution: | 1.Dipartimento di Matematica e Fisica,Università degli Studi della Campania “Luigi Vanvitelli”,Caserta,Italy;2.Department of Geometry, MTA-ELTE Geometric and Algebraic Combinatorics Research Group,ELTE E?tv?s Loránd University,Budapest,Hungary |
| |
Abstract: | The rank of a scattered \({\mathbb F}_q\)-linear set of \({{\mathrm{{PG}}}}(r-1,q^n)\), rn even, is at most rn / 2 as it was proved by Blokhuis and Lavrauw. Existence results and explicit constructions were given for infinitely many values of r, n, q (rn even) for scattered \({\mathbb F}_q\)-linear sets of rank rn / 2. In this paper, we prove that the bound rn / 2 is sharp also in the remaining open cases. Recently Sheekey proved that scattered \({\mathbb F}_q\)-linear sets of \({{\mathrm{{PG}}}}(1,q^n)\) of maximum rank n yield \({\mathbb F}_q\)-linear MRD-codes with dimension 2n and minimum distance \(n-1\). We generalize this result and show that scattered \({\mathbb F}_q\)-linear sets of \({{\mathrm{{PG}}}}(r-1,q^n)\) of maximum rank rn / 2 yield \({\mathbb F}_q\)-linear MRD-codes with dimension rn and minimum distance \(n-1\). |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|