Computer classification of linear codes based on lattice point enumeration and integer linear programming

dc.contributor.authorKurz, Sascha
dc.date.accessioned2024-03-26T10:34:26Z
dc.date.available2024-03-26T10:34:26Z
dc.date.issued2024-03-26
dc.description.abstractLinear codes play a central role in coding theory and have applications in several branches of mathematics. For error correction purposes the minimum Hamming distance should be as large as possible. Linear codes related to applications in Galois Geometry often require a certain divisibility of the occurring weights. In this paper we present an algorithmic framework for the classification of linear codes over finite fields with restricted sets of weights. The underlying algorithms are based on lattice point enumeration and integer linear programming. We present new enumeration and non-existence results for projective two-weight codes, divisible codes, and additive GF(4)-codes.en
dc.identifier.urihttps://open.fau.de/handle/openfau/30815
dc.identifier.urihttps://doi.org/10.25593/open-fau-535
dc.language.isoen
dc.rights.urihttps://creativecommons.org/licenses/by-nc-nd/4.0/
dc.subjectlinear codes
dc.subjectclassification
dc.subjectenumeration
dc.subjectlattice point enumeration
dc.subjectinteger linear programming
dc.subjecttwo-weight codes
dc.titleComputer classification of linear codes based on lattice point enumeration and integer linear programmingen
dc.typepreprint
local.sendToDnbfree
local.subject.fakultaetDepartment of Data Science
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