@misc{10481/108623,
year = {2025},
month = {12},
url = {https://hdl.handle.net/10481/108623},
abstract = {We achieve new results on skew polynomial rings and their quotients, including the
first explicit example of a skew polynomial ring where the ratio of the degree of a skew
polynomial to the degree of its bound is not extremal. These methods lead to the
construction of new (not necessarily associative) division algebras and maximum rank
distance (MRD) codes over both finite and infinite division rings. In particular, we
construct new non-associative division algebras whose right nucleus is a central simple
algebra having degree greater than 1. Over finite fields, we obtain new semifields and
MRD codes for infinitely many choices of parameters. These families extend and contain
many of the best previously known constructions.},
organization = {(GNSAGA - INdAM) - (E53C23001670001)},
organization = {Bando Galileo 2024 - (G24-216)},
organization = {MICIU/AEI/ 10.13039/501100011033 and FEDER - (PID2023-149565NB-I00)},
publisher = {Elsevier},
keywords = {Skew polynomial rings},
keywords = {Division algebra},
keywords = {Semifield},
title = {Quotients of skew polynomial rings: new constructions of division algebras and MRD codes},
doi = {10.1016/j.jalgebra.2025.11.024},
author = {Lobillo Borrero, Francisco Javier and Santonastaso, Paolo and Sheekey, John},
}