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On strongly walk regular graphs,triple sum sets and their codes

DOI zum Zitieren der Version auf EPub Bayreuth: https://doi.org/10.15495/EPub_UBT_00006690
URN to cite this document: urn:nbn:de:bvb:703-epub-6690-8

Title data

Kiermaier, Michael ; Kurz, Sascha ; Solé, Patrick ; Stoll, Michael ; Wassermann, Alfred:
On strongly walk regular graphs,triple sum sets and their codes.
Bayreuth , 2022 . - 42 S.

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Abstract

Strongly walk regular graphs (SWRGs or s-SWRGs) form a natural generalization of strongly regular graphs (SRGs) where paths of length~2 are replaced by paths of length s. They can be constructed as coset graphs of the duals of projective three-weight codes whose weights satisfy a certain equation. We provide classifications of the feasible parameters of these codes in the binary and ternary case for medium size code lengths. For the binary case, the divisibility of the weights of these codes is investigated and several general results are shown. It is known that an s-SWRG has at most 4 distinct eigenvalues k > t_1 > t_2 > t_3$, and that the triple (t_1, t_2, t_3) satisfies a certain homogeneous polynomial equation of degree s-2 (Van Dam, Omidi, 2013). This equation defines a plane algebraic curve; we use methods from algorithmic arithmetic geometry to show that for s=5 and s=7, there are only the obvious solutions, and we conjecture this to remain true for all (odd) s>8.

Further data

Item Type:	Preprint, postprint
Keywords:	strongly walk-regular graphs; triple sum sets; three-weight codes; eigenvalues; plane algebraic curve
Subject classification:	Mathematics Subject Classification Code: 05E30 (11D41 94B05)
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 Mathematics II (Computer Algebra) Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics II (Computer Algebra) > Chair Mathematics II (Computer Algebra) - Univ.-Prof. Dr. Michael Stoll Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematical Economics Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics and Didactics Faculties
Language:	English
Originates at UBT:	Yes
URN:	urn:nbn:de:bvb:703-epub-6690-8
Date Deposited:	11 Oct 2022 06:12
Last Modified:	16 Aug 2023 10:37
URI:	https://epub.uni-bayreuth.de/id/eprint/6690

Available Versions of this Item

On strongly walk regular graphs,triple sum sets and their codes. (deposited 11 Dec 2020 08:47)
- On strongly walk regular graphs,triple sum sets and their codes. (deposited 17 Dec 2021 06:51)
  - On strongly walk regular graphs,triple sum sets and their codes. (deposited 11 Oct 2022 06:12) [Currently Displayed]
    - On strongly walk regular graphs,triple sum sets and their codes. (deposited 17 Aug 2023 07:29)

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