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

2021/08/30 by Marco Timpanella, Timpanella, Marco, Giovanni Zini +1
Computer Science · Engineering · #Advanced Wireless Communication Techniques #Coding theory and cryptography #Combinatorics (math.CO) #Cooperative Communication and Network Coding #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT)

paper · pdf · doi:10.48550/arxiv.2108.13082

openalex publication_date 2021/08/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we consider a family F of 16-dimensional \mathbbF_q-linear rank metric codes in \mathbbF_q^8×8, arising from the polynomial x^qs+δx^q^4+s∈\mathbbF_q⁸[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.

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