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

Pumpluen, Susanne (2017) How to obtain lattices from (f,σ,δ)-codes via a generalization of Construction A. Applicable Algebra in Engineering, Communication and Computing . pp. 1-21. ISSN 1432-0622

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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.

Item Type: Article
Keywords: Space-time block code, linear ((f,σ,δ)-code, nonassociative algebra, coset coding, wiretap coding, Construction A, order, skew polynomial ring
Schools/Departments: University of Nottingham, UK > Faculty of Science > School of Mathematical Sciences
Identification Number: 10.1007/s00200-017-0344-9
Depositing User: Eprints, Support
Date Deposited: 03 Oct 2017 09:00
Last Modified: 20 Oct 2017 18:00
URI: http://eprints.nottingham.ac.uk/id/eprint/46898

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