Three-weight codes over rings and strongly walk regular graphs
Abstract
We construct strongly walk-regular graphs as coset graphs of the duals of codes with three non-zero homogeneous weights over Zpm, 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 Teichm\"uller codes. As a byproduct, we give an alternative proof that the Kerdock code is nonlinear.
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