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(4), 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: Aug 1, 2018
• Deposit Date: Oct 3, 2017
• Publicly Available Date: Oct 16, 2017
• Journal: Applicable Algebra in Engineering, Communication and Computing
• Print ISSN: 0938-1279
• Electronic ISSN: 1432-0622
• Publisher: Springer Verlag
• Peer Reviewed: Peer Reviewed
• Volume: 29
• Issue: 4
• DOI: https://doi.org/10.1007/s00200-017-0344-9
• Keywords: Space-time block code, linear ((f,σ,δ)-code; nonassociative algebra; coset coding, wiretap coding; Construction A; order; skew polynomial ring
• Public URL: https://nottingham-repository.worktribe.com/output/948786
• Publisher URL: https://link.springer.com/article/10.1007%2Fs00200-017-0344-9
• Contract Date: Oct 3, 2017