New semifields and new MRD codes from skew polynomial rings

By John Sheekey. Journal of the London Mathematical Society, 2018

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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.

Subfields: Artificial Intelligence, Discrete Mathematics and Combinatorics, Electrical and Electronic Engineering

View Paper: https://www.semanticscholar.org/paper/0c857c674f221db61d828c9289595f7a9c8df060