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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.
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.
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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