MRD-codes arising from the trinomial x^q+x^q3+cx^q5∈\mathbbF_q⁶[x]

2019/07/18 by Giuseppe Marino, Marino, Giuseppe, Maria Montanucci +3 · 1 citation
Computer Science · Engineering · Mathematics · #Coding theory and cryptography #graph theory and CDMA systems #Finite Group Theory Research

paper · pdf · doi:10.48550/arxiv.1907.08122

Abstract

In [10], the existence of \mathbbF_q-linear MRD-codes of \mathbbF_q^{6× 6}, with dimension 12, minimum distance 5 and left idealiser isomorphic to \mathbbF_q⁶, defined by a trinomial of \mathbbF_q⁶[x], when q is odd and q≡ 0,± 1\pmod 5, has been proved. In this paper we show that this family produces \mathbbF_q-linear MRD-codes of \mathbbF_q^{6× 6}, with the same properties, also in the remaining q odd cases, but not in the q even case. These MRD-codes are not equivalent to the previously known MRD-codes. We also prove that the corresponding maximum scattered \mathbbF_q-linear sets of PG(1,q⁶) are not PΓL(2,q⁶)-equivalent to any previously known scattered linear set.

Cited by

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

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