Three-weight codes over rings and strongly walk regular graphs

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Kiermaier, Michael ; Kurz, Sascha ; Shi, Minjia ; Solé, Patrick:
Three-weight codes over rings and strongly walk regular graphs.
Bayreuth , 2019 . - 28 S.

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Abstract

We construct strongly walk-regular graphs as coset graphs of the duals of codes with three non-zero homogeneous weights over Z_p<sup>m<sup>, for p a prime, and more generally over chain rings of depth m, and with a residue field of size q, a prime power. 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.