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

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Pumpluen, Susanne (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). pp. 313-333. ISSN 1432-0622

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Official URL: https://link.springer.com/article/10.1007%2Fs00200-017-0344-9

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
RIS ID:	https://nottingham-repository.worktribe.com/output/948786
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:	04 May 2020 19:48
URI:	https://eprints.nottingham.ac.uk/id/eprint/46898

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