New maximum scattered linear sets of the projective line
New maximum scattered linear sets of the projective line
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DOI：
10.1016/j.ffa.2018.08.001
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发表时间：
2017-09
期刊：
影响因子：
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通讯作者：
Bence Csajbók;G. Marino;Ferdinando Zullo
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文献类型：
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作者：
Bence Csajbók;G. Marino;Ferdinando Zullo
在[2]和[18]中，给出了射影线PG （1, q n）的最大离散F q线性集的前两族。最近在[22]和[5]中，构造了V （2, qn）的最大离散F - q子空间的新例子，但相应线性集的等价问题仍未解决。这里我们证明在[22]和[5]中，对于n= 6,8， F - q-线性集是新的。此外，对于q奇数，q≡±1,0 (mod 5)，我们给出了PG （1,q 6）中由三叉多项式产生的最大离散F q线性集的新例子，它定义了F q 6× 6的新的F q线性mrd码，其维数为12，最小距离为5，并且左理想子同构于F q 6。
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 6× 6 with dimension 12, minimum distance 5 and left idealiser isomorphic to F q 6.