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|Title:||On construction D and related constructions of lattices from linear codes||Authors:||Kositwattanarerk, Wittawat
|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.||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
|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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