New Bounds for Codes Over Finite Frobenius Rings
Eimear Byrne, Marcus Greferath, Axel Kohnert, Vitaly Skachek
TL;DR
This paper investigates the limits of linear codes over finite Frobenius rings using homogeneous weight, improving existing bounds and proposing new ones, with examples of codes that meet these bounds.
Contribution
It introduces improved bounds for codes over finite Frobenius rings and presents families of codes that achieve these bounds.
Findings
Enhanced Plotkin bound for these codes
Proposed Singleton bound for codes over Frobenius rings
Examples of codes meeting the new bounds
Abstract
We give results on the question of code optimality for linear codes over finite Frobenius rings for the homogeneous weight. This article improves on the existing Plotkin bound derived in an earlier paper, and suggests a version of a Singleton bound. We also present some families of codes meeting these new bounds.
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Taxonomy
TopicsCoding theory and cryptography · graph theory and CDMA systems · Finite Group Theory Research