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A generalization of the cylinder conjecture for divisible codes

DOI zum Zitieren der Version auf EPub Bayreuth: https://doi.org/10.15495/EPub_UBT_00005152
URN to cite this document: urn:nbn:de:bvb:703-epub-5152-1

Title data

Kurz, Sascha ; Mattheus, Sam:
A generalization of the cylinder conjecture for divisible codes.
Bayreuth , 2020 . - 16 S.

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Abstract

We extend the original cylinder conjecture on point sets in affine three-dimensional space to the more general framework of divisible linear codes over GF(q) and their classification. Through a mix of linear programming, combinatorial techniques and computer enumeration, we investigate the structural properties of these codes. In this way, we can prove a reduction theorem for a generalization of the cylinder conjecture, show some instances where it does not hold and prove its validity for small values of q. In particular, we correct a flawed proof for the original cylinder conjecture for q=5 and present the first proof for q=7.

Further data

Item Type: Preprint, postprint
Keywords: cylinder conjecture, linear codes, divisible codes
Subject classification: Mathematics Subject Classification Code: 05B25 (51D20 51E22)
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-5152-1
Date Deposited: 06 Nov 2020 10:37
Last Modified: 06 Nov 2020 10:37
URI: https://epub.uni-bayreuth.de/id/eprint/5152

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