Codes over \(\mathbb F_{3} + u\mathbb F_{3}\) and improvements to the bounds on ternary linear codes
type: Item
instance of: scholarly article
title: Codes over \(\mathbb F_{3} + u\mathbb F_{3}\) and improvements to the bounds on ternary linear codes
zbMATH Open document ID: 0961.94013
DOI: 10.1023/A:1008355310919
author: T. Aaron Gulliver
author: Masaaki Harada
published in: Designs, Codes and Cryptography
publication date: 2001-02-18T00:00:00Z
review text: It is shown that a linear code with length \(n\) and Gray distance \(d\) over the ring \(\mathbb F_3 + u\mathbb F_3\) of order 9 can (using a Gray map) be mapped into a ternary linear code of length \(2n\), Hamming distance \(d\), and the same cardinality. A computer search for quasi-cyclic codes over \(\mathbb F_3 + u\mathbb F_3\) has been carried out; the results of this search lead to good (quasi-cyclic) ternary codes, six of which improve on the best known lower bound on the maximum possible minimum Hamming distance: \([208,8,127]\), \([150,10,85]\), \([160,10,91]\), \([170,10,97]\), \([180,10,103]\), \([190,10,110]\).
Mathematics Subject Classification ID: 94B05
Mathematics Subject Classification ID: 94B65
zbMATH DE Number: 1565474
zbMATH Keywords: codes over rings
zbMATH Keywords: ternary linear codes
reviewed by: Patric R. J. Östergård
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1565474