On two-weight $$\mathbb {Z}_{2^k}$$ Z 2 k -codes

Abstract

We determine the possible homogeneous weights of regular projective two-weight codes over $$\mathbb {Z}_{2^k}$$ of length $$n>3$$ , with dual Krotov distance $$d^{\lozenge }$$ at least four. The determination of the weights is based on parameter restrictions for strongly regular graphs applied to the coset graph of the dual code. When $$k=2$$ , we characterize the parameters of such codes as those of the inverse Gray images of $$\mathbb {Z}_4$$ -linear Hadamard codes, which have been characterized by their types by several authors.