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

08/30/2021

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by   Marco Timpanella, et al.

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In this paper we consider a family ℱ of 16-dimensional 𝔽_q-linear rank metric codes in 𝔽_q^8×8, arising from the polynomial x^q^s+δ x^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.