On bounds for codes over Frobenius rings under homogeneous weights (original) (raw)

Homogeneous weight functions were introduced by Heise and Constantinescu (Lineare Codes über Restklassenringen ganzer Zahlen und ihre Automorphismen bezüglich einer verallgemeinerten Hamming-Metrik, Ph.D. Thesis, Technische Universität München, 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.