Abstract
This talk is an overview of codes that are defined as modules over skew polynomial rings. These codes can be seen as a generalization of cyclic codes or more generally polynominal codes to a non commutative polynomial ring. Most properties of classical cyclic codes can be generalized to this new setting and self-dual codes can be easily identified. Those rings are no longer unique factorization rings, therefore there are many factors of X n − 1, each generating a “skew cyclic code”. In previous works many new codes and new self-dual codes with a better distance than existing codes have been found. Recently cyclic and skew-cyclic codes over rings have been extensively studied in order to obtain codes over subfields (or subrings) under mapping with good properties.
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Ulmer, F. (2015). Extended Abstract: Codes as Modules over Skew Polynomial Rings. In: El Hajji, S., Nitaj, A., Carlet, C., Souidi, E. (eds) Codes, Cryptology, and Information Security. C2SI 2015. Lecture Notes in Computer Science(), vol 9084. Springer, Cham. https://doi.org/10.1007/978-3-319-18681-8_7
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DOI: https://doi.org/10.1007/978-3-319-18681-8_7
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