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Three-Weight Codes over Rings and Strongly Walk Regular Graphs.
- Source :
-
Graphs & Combinatorics . Jun2022, Vol. 38 Issue 3, p1-23. 23p. - Publication Year :
- 2022
-
Abstract
- 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. [ABSTRACT FROM AUTHOR]
- Subjects :
- *REGULAR graphs
*DIOPHANTINE equations
*CLASSIFICATION
Subjects
Details
- Language :
- English
- ISSN :
- 09110119
- Volume :
- 38
- Issue :
- 3
- Database :
- Academic Search Index
- Journal :
- Graphs & Combinatorics
- Publication Type :
- Academic Journal
- Accession number :
- 155759010
- Full Text :
- https://doi.org/10.1007/s00373-021-02430-6