Some results on NQR codes
type: Item
instance of: scholarly article
title: Some results on NQR codes
zbMATH Open document ID: 0934.94017
DOI: 10.1023/A:1008387423552
author: M. C. Bhandari
author: M. K. Gupta
author: Arbind Kumar Lal
published in: Designs, Codes and Cryptography
publication date: 2000-02-04T00:00:00Z
review text: \textit{P. D. Tiu} and \textit{D. T. Wallace} [IEEE Trans. Inf. Theory 40, 946-949 (1994; Zbl 0824.94028)] have constructed a new class of linear codes called norm quadratic residue codes \(C_p\) for \(p\) a prime of the form \(4n+1\). They have shown that \(\dim C_p\leq p\), minimum distance \(d\geq p-1\), \(C_p\) is weakly self dual and the weight of each codeword is divisible by 4. In the present paper the authors show that a similar construction works for primes of the form \(4n-1\). They collect some more results for any odd prime \(p\). In the paper it is shown that \(\dim C_p=p\), \(C_p\) is normal and its covering radius is \(\frac{p(p-1)}{2}\).
Mathematics Subject Classification ID: 94B05
Mathematics Subject Classification ID: 94B40
Mathematics Subject Classification ID: 94B75
zbMATH DE Number: 1275099
zbMATH Keywords: norm quadratic residue codes
zbMATH Keywords: covering radius
MaRDI profile type: Publication
full work available at URL: a:1008387423552
OpenAlex ID: W1646844369
description: scientific article; zbMATH DE number 1275099