New bounds for codes over finite Frobenius rings

New bounds for codes over finite Frobenius rings

We give further 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 [6], and suggests a version of a Singleton bound. We also present some families of codes meeting these new bounds.

Singleton Bounds for Codes over Finite Rings

We introduce the Singleton bounds for codes over a finite commutative quasi-Frobenius ring.

Witt Theorems for Linear Codes over Finite Frobenius Rings

Matrix product codes over finite commutative Frobenius rings

Properties of matrix product codes over finite commutative Frobenius rings are investigated. The minimum distance of matrix product codes constructed with several types of matrices is bounded in different ways. The duals of matrix product codes are also explicitly described in terms of matrix product codes.

On Plotkin-Optimal Codes over Finite Frobenius Rings

We study the Plotkin bound for codes over a finite Frobenius ring R equipped with the homogeneous weight. We show that for codes meeting the Plotkin bound, the distribution on R induced by projection onto a coordinate has an interesting property. We present several constructions of codes meeting the Plotkin bound and of Plotkin-optimal codes. We also investigate the relationship between Butson-...