On p-ary local frobenius rings and their homogeneous weights

In this work, a characterization of different properties of p-ary local Frobenius rings and their generating characters is given. Using the generating character, a general form for the homogeneous weights of such rings is described. In particular it is shown that the homogenous weights of all such rings have two non-zero values. Moreover, distance-preserving, linear Gray maps for the homogeneous weights of some classes of p-ary local Frobenius rings are found and using the Gray image, many linear p-ary codes attaining the Griesmer bound are counstructed.