How to obtain lattices from ( f, σ, δ)-codes via a generalization of Construction A

Pumpluen, Susanne

Abstract

We show how cyclic ( f, σ, δ)-codes over finite rings canonically induce a Z lattice in RN by using certain quotients of orders in nonassociative division algebras defined using the skew polynomial f . This construction generalizes the one using certain σ-constacyclic codes by Ducoat and Oggier, which used quotients of orders in non-commutative associative division algebras defined by f , and can be viewed as a generalization of the classical Construction A for lattices from linear codes. It has the potential to be applied to coset coding, in particular to wire-tap coding. Previous results by Ducoat and Oggier are obtained as special cases.

Citation

Pumpluen, S. (2018). How to obtain lattices from ( f, σ, δ)-codes via a generalization of Construction A. Applicable Algebra in Engineering, Communication and Computing, 29, 313-333. https://doi.org/10.1007/s00200-017-0344-9

• Journal Article Type: Article
• Acceptance Date: Sep 29, 2017
• Online Publication Date: Oct 16, 2017
• Publication Date: 2018-08
• Deposit Date: Mar 23, 2024
• Publicly Available Date: May 1, 2024
• Journal: Applicable Algebra in Engineering, Communication and Computing
• Print ISSN: 0938-1279
• Publisher: Springer Verlag
• Peer Reviewed: Peer Reviewed
• Volume: 29
• Pages: 313-333
• DOI: https://doi.org/10.1007/s00200-017-0344-9
• Keywords: Information Theory; Rings and Algebras
• Public URL: https://nottingham-repository.worktribe.com/output/2461434