RT info:eu-repo/semantics/bookPart
T1 The metric structure of linear codes
A1 Ruano Benito, Diego
AB The bilinear form with associated identity matrix is used in coding  theory to define the dual code of a linear code, also it endows linear codes with a metric space structure. This metric structure was studied for generalized toric codes and a characteristic decomposition was obtained, which led to several applications as the construction of stabilizer quantum codes and LCD codes. In this work, we use the study of bilinear forms over a finite field to give a decomposition of an arbitrary linear code similar to the one obtained for generalized toric codes. Such a decomposition, called the geometric decomposition of a linear code, can be obtained in a constructive way; it allows us to express easily the dual code of a linear code and provides a method to construct stabilizer quantum codes, LCD codes and in some cases, a method to estimate their minimum distance. The proofs for  characteristic 2 are different, but they are developed in parallel.
PB Springer
YR 2018
FD 2018
LK http://uvadoc.uva.es/handle/10324/31741
UL http://uvadoc.uva.es/handle/10324/31741
LA eng
NO The metric structure of linear codes. In Singularities, Algebraic Geometry, Commutative Algebra, and Related Topics, pages 537-561. Editors: G.-M. Greuel, L. Narváez Macarro, S. Xambó-Descamps. Springer Verlag. ISBN: 978-3-319-96826-1 (2018)
NO Producción Científica
DS UVaDOC
RD 20-abr-2024