In [2] and [18] are presented the first two families of maximum scattered Fq-linear sets of the projective line PG(1,q^n). More recently in [22] and in [5], new examples of maximum scattered Fq-subspaces of V(2,q^n) have been constructed, but the equivalence problem of the corresponding linear sets is left open. Here we show that the Fq-linear sets presented in [22] and in [5], for n=6,8, are new. Also, for q odd, q≡±1,0 (mod 5), we present new examples of maximum scattered Fq-linear sets in PG(1,q^6), arising from trinomial polynomials, which define new Fq-linear MRD-codes of Fq^(6×6) with dimension 12, minimum distance 5 and left idealiser isomorphic to Fq^6.
New maximum scattered linear sets of the projective line / Csajbok, Bence; Marino, Giuseppe; Zullo, Ferdinando. - In: FINITE FIELDS AND THEIR APPLICATIONS. - ISSN 1071-5797. - STAMPA. - 54:(2018), pp. 133-150. [10.1016/j.ffa.2018.08.001]
New maximum scattered linear sets of the projective line
Csajbok, Bence
;
2018-01-01
Abstract
In [2] and [18] are presented the first two families of maximum scattered Fq-linear sets of the projective line PG(1,q^n). More recently in [22] and in [5], new examples of maximum scattered Fq-subspaces of V(2,q^n) have been constructed, but the equivalence problem of the corresponding linear sets is left open. Here we show that the Fq-linear sets presented in [22] and in [5], for n=6,8, are new. Also, for q odd, q≡±1,0 (mod 5), we present new examples of maximum scattered Fq-linear sets in PG(1,q^6), arising from trinomial polynomials, which define new Fq-linear MRD-codes of Fq^(6×6) with dimension 12, minimum distance 5 and left idealiser isomorphic to Fq^6.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
