Given an F-represented matroid (M,ρ) with the ground set [m], representation ρ naturally defines a hyperplane arrangement Aρ. We will study its parallel translates Aρ,g of Aρ for all g∈Fm. Its intersection semi-lattices L(Aρ,g) and characteristic polynomials χ(Aρ,g,t) be classified by lattice derived Aδρ, which is associated (δM,δρ) also known as discriminantal in literature. As byproduct, we o...

We give a method to compute the complete weight distribution of translates of linear codes over Z4. The method follows known ideas that have already been used successfully by others for Hamming weight distributions. For the particular case of quaternary Preparata codes, we obtain that the number of distinct complete weights for the dual Preparata codes and the number of distinct complete coset ...