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https://hdl.handle.net/10356/95282
Title: | On construction D and related constructions of lattices from linear codes | Authors: | Kositwattanarerk, Wittawat Oggier, Frederique |
Keywords: | DRNTU::Engineering::Civil engineering::Construction technology | Issue Date: | 2013 | Source: | 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. | Conference: | International Workshop on Coding and Cryptography (2013 : Bergen, Norway) | Abstract: | 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. | URI: | https://hdl.handle.net/10356/95282 http://hdl.handle.net/10220/10104 |
Schools: | School of Physical and Mathematical Sciences | Rights: | © 2013 The International Workshop on Coding and Cryptography(WCC 13). | Fulltext Permission: | none | Fulltext Availability: | No Fulltext |
Appears in Collections: | SPMS Conference Papers |
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