On minimum weight codewords in QR codes
type: Item
instance of: scholarly article
title: On minimum weight codewords in QR codes
zbMATH Open document ID: 0643.94015
DOI: 10.1016/0097-3165(88)90078-7
author: Donald W. Newhart
published in: Journal of Combinatorial Theory. Series A
publication date: 1988-01-01T00:00:00Z
review text: A linear (n,k,d) code is said to be optimal iff \(d=n-k+1\). Assmus and Mattson have shown that given a prime p, for all but a finite number of primes q each cyclic (p,k) code over \(GF(q^ i)\) is optimal. This paper provides a method for determining these ``exceptional'' characteristics, and the corresponding minimum weights, for quadratic-residue (QR) codes of modest length. The procedure involves calculations with global QR codes. The analysis reveals that a nonoptimal case requires \(q\leq 2^{- (p-1)/2}[(p+1)/2]^{(p+1)/4}.\) In addition, the method can be used to examine the t-designs derived from the codewords of minimum weight.
Mathematics Subject Classification ID: 94B15
zbMATH DE Number: 4049545
zbMATH Keywords: optimal codes
zbMATH Keywords: quadratic-residue codes
zbMATH Keywords: information sets
zbMATH Keywords: t-designs
MaRDI profile type: Publication
full work available at URL: 0097-3165(88)90078-7
OpenAlex ID: W2034437575
cites work: New 5-designs
cites work: On weights in quadratic-residue codes
cites work: Information sets in quadratic-residue codes
cites work: Q3939714
cites work: On MDS extensions of generalized Reed- Solomon codes
cites work: Q4200153
description: scientific article; zbMATH DE number 4049545