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A Generalization of the Cylinder Conjecture for Divisible Codes

Title data

Kurz, Sascha ; Mattheus, Sam:
A Generalization of the Cylinder Conjecture for Divisible Codes.
In: IEEE Transactions on Information Theory. Vol. 68 (2022) Issue 4 . - pp. 2281-2289.
ISSN 0018-9448
DOI: https://doi.org/10.1109/TIT.2021.3134201

Abstract in another language

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: Article in a journal
Refereed: Yes
Keywords: cylinder conjecture; linear codes; divisible codes
Subject classification: Mathematics Subject Classification Code: 05B25 (51D20 51E22)
Institutions of the University: Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematical Economics
Result of work at the UBT: Yes
DDC Subjects: 000 Computer Science, information, general works > 004 Computer science
500 Science > 510 Mathematics
Date Deposited: 22 Mar 2022 10:15
Last Modified: 22 Mar 2022 10:15
URI: https://eref.uni-bayreuth.de/id/eprint/68965