On the existence of MRD self-dual codes

2023/12/18 by Grégory Berhuy, Berhuy, Grégory
Computer Science · #Advanced Data Storage Technologies #Coding theory and cryptography #FOS: Computer and information sciences #Information Theory (cs.IT) #Primary: 94B05 #Secondary: 11E04

paper · pdf · doi:10.48550/arxiv.2312.11341

openalex publication_date 2023/12/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we investigate the existence of self-dual MRD codes C⊂ Lⁿ, where L/F is an arbitrary field extension of degree m≥ n. We then apply our results to the case of finite fields, and prove that if m=n and F=\mathbbF_q, a self-dual MRD code exists if and only if q≡ n≡ 3 [4].

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