Extension Theorems for Various Weight Functions over Frobenius Bimodules

TL;DR

This paper investigates extension theorems for different weight functions on codes over Frobenius bimodules, providing character-theoretic proofs and extending known results to new weights.

Contribution

It introduces a character-theoretic approach and duality theory to establish extension properties for various weights on Frobenius bimodule codes, including new weights.

Findings

Hamming and homogeneous weights satisfy the extension property

Extension property established for Rosenbloom-Tsfasman weight

Character-theoretic methods provide alternative proofs

Abstract

In this paper we study codes where the alphabet is a finite Frobenius bimodule over a finite ring. We discuss the extension property for various weight functions. Employing an entirely character-theoretic approach and a duality theory for partitions on Frobenius bimodules we derive alternative proofs for the facts that the Hamming weight and the homogeneous weight satisfy the extension property. We also use the same techniques to derive the extension property for other weights, such as the Rosenbloom-Tsfasman weight.