A Griesmer bound for linear codes over finite quasi-Frobenius rings

Witt Theorems for Linear Codes over Finite Frobenius Rings

Linear Codes over Finite Rings

Linear codes over finite rings with identity have recently raised a great interest for their new role in algebraic coding theory and for their successful application in combined coding and modulation. Thus, in this paper we address the problems of constructing of new cyclic, BCH, alternant, Goppa and Srivastava codes over local finite commutative rings with identity. These constructions are ver...

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.

Quasi-Cyclic Codes Over Finite Chain Rings

In this paper, we mainly consider quasi-cyclic (QC) codes over finite chain rings. We study module structures and trace representations of QC codes, which lead to some lower bounds on the minimum Hamming distance of QC codes. Moreover, we investigate the structural properties of 1-generator QC codes. Under some conditions, we discuss the enumeration of 1-generator QC codes and describe how to o...

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.