New maximum scattered linear sets of the projective line

Csajbók, Bence and Marino, G. and Zullo, F. (2018) New maximum scattered linear sets of the projective line. FINITE FIELDS AND THEIR APPLICATIONS, 54. pp. 133-150. ISSN 1071-5797

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Abstract

In [2] and [18] are presented the first two families of maximum scattered F-q-linear sets of the projective line PG(1, q(n)). More recently in [22] and in [5], new examples of maximum scattered F-q-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 F-q-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 F-q-linear sets in PG(1, q(6)), arising from trinomial polynomials, which define new F-q-linear MRD-codes of F-q(6x6) with dimension 12, minimum distance 5 and left idealiser isomorphic to F-q6. (C) 2018 Elsevier Inc. All rights reserved.

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