On construction D and related constructions of lattices from linear codes

We investigate three closely related constructions of lattices from linear codes: the classical Construction D, Construction D ̅, and the recently developed Construction A’. These constructions have been proven useful and result in efficient encoding and decoding algorithms for Barnes-Wall lattices...

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Main Authors: Kositwattanarerk, Wittawat, Oggier, Frederique
Other Authors: School of Physical and Mathematical Sciences
Format: Conference or Workshop Item
Language:English
Published: 2013
Subjects:
Online Access:https://hdl.handle.net/10356/95282
http://hdl.handle.net/10220/10104
http://www.selmer.uib.no/WCC2013/
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Institution: Nanyang Technological University
Language: English
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spelling sg-ntu-dr.10356-952822019-12-06T19:11:48Z On construction D and related constructions of lattices from linear codes Kositwattanarerk, Wittawat Oggier, Frederique School of Physical and Mathematical Sciences International Workshop on Coding and Cryptography (2013 : Bergen, Norway) DRNTU::Engineering::Civil engineering::Construction technology We investigate three closely related constructions of lattices from linear codes: the classical Construction D, Construction D ̅, and the recently developed Construction A’. These constructions have been proven useful and result in efficient encoding and decoding algorithms for Barnes-Wall lattices. Here we analyze their applications in a general setting. We show that Construction D ̅ produces a lattice packing if and only if the nested codes being used are closed under Schur product, thus proving the similarity of Construction D and Construction D ̅ when applied to Reed-Muller codes. In addition, we provide a correspondence between nested binary linear codes and codes over polynomial rings. This proves that Construction A’ does not always produce a lattice, but any lattices constructible using Construction D ̅ are also constructible using Construction A’. This result also gives a partial condition for Construction A’ to produce a lattice. 2013-06-10T03:52:12Z 2019-12-06T19:11:48Z 2013-06-10T03:52:12Z 2019-12-06T19:11:48Z 2013 2013 Conference Paper Kositwattanarerk, W., & Oggier, F. (2013). On Construction D and Related Constructions of Lattices from Linear Codes. The International Workshop on Coding and Cryptography(WCC 13), 427-436. https://hdl.handle.net/10356/95282 http://hdl.handle.net/10220/10104 http://www.selmer.uib.no/WCC2013/ 169365 en © 2013 The International Workshop on Coding and Cryptography(WCC 13).
institution Nanyang Technological University
building NTU Library
country Singapore
collection DR-NTU
language English
topic DRNTU::Engineering::Civil engineering::Construction technology
spellingShingle DRNTU::Engineering::Civil engineering::Construction technology
Kositwattanarerk, Wittawat
Oggier, Frederique
On construction D and related constructions of lattices from linear codes
description We investigate three closely related constructions of lattices from linear codes: the classical Construction D, Construction D ̅, and the recently developed Construction A’. These constructions have been proven useful and result in efficient encoding and decoding algorithms for Barnes-Wall lattices. Here we analyze their applications in a general setting. We show that Construction D ̅ produces a lattice packing if and only if the nested codes being used are closed under Schur product, thus proving the similarity of Construction D and Construction D ̅ when applied to Reed-Muller codes. In addition, we provide a correspondence between nested binary linear codes and codes over polynomial rings. This proves that Construction A’ does not always produce a lattice, but any lattices constructible using Construction D ̅ are also constructible using Construction A’. This result also gives a partial condition for Construction A’ to produce a lattice.
author2 School of Physical and Mathematical Sciences
author_facet School of Physical and Mathematical Sciences
Kositwattanarerk, Wittawat
Oggier, Frederique
format Conference or Workshop Item
author Kositwattanarerk, Wittawat
Oggier, Frederique
author_sort Kositwattanarerk, Wittawat
title On construction D and related constructions of lattices from linear codes
title_short On construction D and related constructions of lattices from linear codes
title_full On construction D and related constructions of lattices from linear codes
title_fullStr On construction D and related constructions of lattices from linear codes
title_full_unstemmed On construction D and related constructions of lattices from linear codes
title_sort on construction d and related constructions of lattices from linear codes
publishDate 2013
url https://hdl.handle.net/10356/95282
http://hdl.handle.net/10220/10104
http://www.selmer.uib.no/WCC2013/
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