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Three-Weight Codes over Rings and Strongly Walk Regular Graphs

Title data

Shi, Minjia ; Kiermaier, Michael ; Kurz, Sascha ; Sole, Patrick:
Three-Weight Codes over Rings and Strongly Walk Regular Graphs.
In: Graphs and Combinatorics. Vol. 38 (14 March 2022) . - pp. 1-23.
ISSN 1435-5914
DOI: https://doi.org/10.1007/s00373-021-02430-6

Official URL: Volltext

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
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 Mar 2022 10:11
URI: https://eref.uni-bayreuth.de/id/eprint/68964