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Algebraic structures of MRD codes. (English) Zbl 1348.94102

Summary: Based on results in finite geometry we prove the existence of MRD codes in \((\mathbb{F}_q)_{n,n}\) 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.

MSC:

94B27 Geometric methods (including applications of algebraic geometry) applied to coding theory
11T71 Algebraic coding theory; cryptography (number-theoretic aspects)

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References:

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