Algebraic structures of MRD Codes

2015/01/16 by Javier de la Cruz, de la Cruz, Javier, Kiermaier, Michael +4 · 2 citations
Computer Science · Mathematics · #15B33 (Secondary) #16Y60 (Primary) #94B99 #Coding theory and cryptography #Combinatorics (math.CO) #Cooperative Communication and Network Coding #FOS: Computer and information sciences #FOS: Mathematics #Finite Group Theory Research #Information Theory (cs.IT) #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.1502.02711

openalex publication_date 2015/01/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Based on results in finite geometry we prove the existence of MRD codes in (F_q)_(n,n) with minimum distance n which are essentially different from Gabidulin codes. The construction results from algebraic structures which are closely related to those of finite fields. Some of the results may be known to experts, but to our knowledge have never been pointed out explicitly in the literature.

Citations

• On self-dual MRD codes

Cited by

• Skew polynomial representations of matrix algebras and applications to coding theory
• The isotopy classes of Petit division algebras

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• MRD Codes: Constructions and Connections
• A remark on \mathbb F_qⁿ-Linear MRD codes
• On the existence of MRD self-dual codes
• On 3-dimensional MRD codes of type ⟨ x^qt,x+δx^q^2t,G(x) ⟩
• MDS codes over finite fields