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 p.
DOI: https://doi.org/10.15495/EPub_UBT_00006690
Abstract in another language
Strongly walk regular graphs (SWRGs or sSWRGs) 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 threeweight 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 sSWRG 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 s2 (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
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On strongly walk regular graphs,triple sum sets and their codes. (deposited 12 Dec 2020 22:00)

On strongly walk regular graphs, triple sum sets and their codes. (deposited 17 Dec 2021 06:58)
 On strongly walk regular graphs, triple sum sets and their codes. (deposited 11 Oct 2022 06:18) [Currently Displayed]

On strongly walk regular graphs, triple sum sets and their codes. (deposited 17 Dec 2021 06:58)