On bounds for codes over Frobenius rings under homogeneous weights

Homogeneous weight functions were introduced by Heise and Constantimescu (Lineare Codes fiber Restklassenringen ganzer Zahlen und ihre Automorphismen bezijglich einer verallgemeinerten Hamming-Metrik, Ph.D. Thesis, Technische Universitat Munchen, 1995; Problemy Peredachi Informatsii 33(3) (1997) 22-28). They appear as a natural generalization of the Hamming weight on finite fields and the Lee weight on Z(4) and have proven to be important in further papers (J. Combin. Theory 92 (2000) 17-28). This article develops a Plotkin and an Elias bound for (not necessarily linear) block codes on finite Frobenius rings that are equipped with this weight. (C) 2004 Elsevier B.V. All rights reserved.