On (partial) unit memory codes based on Gabidulin codes
type: Item
instance of: scholarly article
title: On (partial) unit memory codes based on Gabidulin codes
zbMATH Open document ID: 1248.94117
DOI: 10.1134/S0032946011020049
author: D. Kharzeev
published in: Problems of Information Transmission
publication date: 2012-03-13T00:00:00Z
review text: The authors consider unit memory and partial unit memory convolutional codes. These rank-\(k/n\) codes have memory 1 and overall constraint length \(\nu=k\) (unit memory codes) or \(\nu<k\) (partial unit memory codes). Thus a (partial) unit memory code has a \(k \times n\) generator matrix of polynomials of degree at most 1. Since the memory is 1, the generator matrix may be given in the form \(G_0+G_1\cdot D\) where \(G_0\), \(G_1\) are scalar matrices of size \(k \times n\). Upper bounds on the free rank distance and slope of unit memory and partial unit memory codes are given. The authors also give a construction for unit memory and partial unit memory codes based on Gabidulin codes, which are certain block codes defined in terms of a parity check matrix. This construction meets the free rank distance upper bound and reaches half of the slope upper bound.
reviewed by: Paul A. Weiner
Mathematics Subject Classification ID: 94B10
Mathematics Subject Classification ID: 94B65
zbMATH DE Number: 6014354
zbMATH Keywords: unit memory codes
zbMATH Keywords: Gabidulin codes
zbMATH Keywords: sum rank metric
MaRDI profile type: Publication
cites work: Optical pulse timing resolution (Corresp.)
cites work: Some optimal partial-unit-memory codes (Corresp.)
cites work: On periodic (partial) unit memory codes with maximum free distance
cites work: Finite-state codes
cites work: Bounded distance decoding of unit memory codes
cites work: Bounds on distances and error exponents of unit memory codes
cites work: Coding for Errors and Erasures in Random Network Coding
cites work: A Rank-Metric Approach to Error Control in Random Network Coding
cites work: Bilinear forms over a finite field, with applications to coding theory
cites work: Theory of codes with maximum rank distance
cites work: Maximum-rank array codes and their application to crisscross error correction
cites work: Q3509721
cites work: Q4256362
cites work: Convolutional codes I: Algebraic structure
cites work: Bounded minimum distance decoding of unit memory codes
full work available at URL: s0032946011020049
OpenAlex ID: W2148957188
description: scientific article; zbMATH DE number 6014354