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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| Other Authors: | |
| Format: | Conference Paper |
| Language: | English |
| Published: |
2013
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| Online Access: | https://hdl.handle.net/10356/95282 http://hdl.handle.net/10220/10104 http://www.selmer.uib.no/WCC2013/ |
| _version_ | 1811685597146775552 |
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| author | Kositwattanarerk, Wittawat Oggier, Frederique |
| author2 | School of Physical and Mathematical Sciences |
| author_facet | School of Physical and Mathematical Sciences Kositwattanarerk, Wittawat Oggier, Frederique |
| author_sort | Kositwattanarerk, Wittawat |
| collection | NTU |
| 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. |
| first_indexed | 2024-10-01T04:47:03Z |
| format | Conference Paper |
| id | ntu-10356/95282 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T04:47:03Z |
| publishDate | 2013 |
| record_format | dspace |
| spelling | ntu-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). |
| spellingShingle | DRNTU::Engineering::Civil engineering::Construction technology Kositwattanarerk, Wittawat Oggier, Frederique On construction D and related constructions of lattices from linear codes |
| title | 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_short | On construction D and related constructions of lattices from linear codes |
| title_sort | on construction d and related constructions of lattices from linear codes |
| topic | DRNTU::Engineering::Civil engineering::Construction technology |
| url | https://hdl.handle.net/10356/95282 http://hdl.handle.net/10220/10104 http://www.selmer.uib.no/WCC2013/ |
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