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

DOI zum Zitieren der Version auf EPub Bayreuth: https://doi.org/10.15495/EPub_UBT_00007636
URN to cite this document: urn:nbn:de:bvb:703-epub-7636-9

Title data

Kurz, Sascha:
Computer classification of linear codes based on lattice point enumeration and integer linear programming.
Bayreuth , 2024 . - 7 S.

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Abstract

Linear 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.

Further data

Item Type:	Preprint, postprint
Keywords:	linear codes; classification; enumeration; lattice point enumeration; integer linear programming; two-weight codes
Subject classification:	Mathematics Subject Classification Code: 94B05 (05E20)
DDC Subjects:	000 Computer Science, information, general works > 004 Computer science 500 Science > 510 Mathematics
Institutions of the University:	Faculties > Faculty of Mathematics, Physics und Computer Science Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematical Economics Faculties
Language:	English
Originates at UBT:	Yes
URN:	urn:nbn:de:bvb:703-epub-7636-9
Date Deposited:	27 Mar 2024 07:29
Last Modified:	27 Mar 2024 07:30
URI:	https://epub.uni-bayreuth.de/id/eprint/7636

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