New semifields and new MRD codes from skew polynomial rings

New semifields and new MRD codes from skew polynomial rings

In this article, we construct a new family of semifields, containing and extending two well‐known families, namely Albert's generalised twisted fields and Petit's cyclic semifields (also known as Johnson–Jha semifields). The construction also gives examples of semifields with parameters fo...

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Veröffentlicht in:Journal of the London Mathematical Society 2020-02, Vol.101 (1), p.432-456
1. Verfasser: Sheekey, John
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description In this article, we construct a new family of semifields, containing and extending two well‐known families, namely Albert's generalised twisted fields and Petit's cyclic semifields (also known as Johnson–Jha semifields). The construction also gives examples of semifields with parameters for which no examples were previously known. In the case of semifields two dimensions over a nucleus and four‐dimensional over their centre, the construction gives all possible examples. Furthermore we embed these semifields in a new family of maximum rank‐distance codes, encompassing most known current constructions, including the (twisted) Delsarte–Gabidulin codes, and containing new examples for most parameters.
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title New semifields and new MRD codes from skew polynomial rings
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