Three-weight codes over rings and strongly walk regular graphs *

International audienceWe 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