On a family of linear MRD codes with parameters $[8\times8,16,7]_q$

Abstract

In this paper we consider a family F of 16-dimensional Fq-linear rank metric codes in F 8×8 q , arising from the polynomial x q s + δx q 4+s ∈ F q 8 [x]. Examples of MRD codes in F have been provided by Csajbók, Marino, Polverino and Zanella (2018). For any large enough odd q, we determine exactly which codes in F are MRD. We also show that the MRD codes in F are not equivalent to any other MRD codes known so far.