at Google ScholarTitle data
Shi, Minjia ; Kiermaier, Michael ; Kurz, Sascha ; Solé, Patrick:
Three-Weight Codes over Rings and Strongly Walk Regular Graphs.
In: Graphs and Combinatorics.
Vol. 38
(2022)
.
- No. 56.
ISSN 1435-5914
DOI: https://doi.org/10.1007/s00373-021-02430-6
Abstract in another language
We construct strongly walk-regular graphs as coset graphs of the duals of codes with three non-zero homogeneous weights over Z_p^m, for p a prime, and more generally over chain rings of depth m, and with a residue field of size q, a prime power. In the case of p=m=2, strong necessary conditions (diophantine equations) on the weight distribution are derived, leading to a partial classification in modest length. Infinite families of examples are built from Kerdock and generalized Teichmüller codes. As a byproduct, we give an alternative proof that the Kerdock code is nonlinear.
Further data
| Item Type: | Article in a journal |
|---|---|
| Refereed: | Yes |
| Keywords: | Strongly walk-regular graphs; Three-weight codes; Homogeneous weight; Kerdock codes; Teichmüller codes |
| Subject classification: | Mathematics Subject Classification Code: 05E30 (94B05) |
| Institutions of the University: | Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematical Economics Faculties Faculties > Faculty of Mathematics, Physics und Computer Science Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics |
| 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 10:11 |
| Last Modified: | 22 Nov 2022 12:16 |
| URI: | https://eref.uni-bayreuth.de/id/eprint/68964 |