<abstract xmlns="http://www.w3.org/1999/xhtml"><p>Since coding has become a basic tool for practically all communication/electronic devices, it is important to carefully study the error patterns that actually occur. This allows correction of only partial errors rather than those which have been studied using Hamming distance, in non-binary cases. </p><p>The paper considers a class of distances, SK-distances, in terms of which partial errors can be defined. Examining the sufficient condition for the existence of a parity check matrix for a given number of parity-checks, the paper contains an upper bound on the number of parity check digits for linear codes with property that corrects all partial random errors of an (n, k ) code with minimum SK-distance at least d. The result generalizes the rather widely used Varshamov-Gilbert bound, which follows from it as a particular case.</p></abstract>

Since coding has become a basic tool for practically all communication/electronic devices, it is important to carefully study the error patterns that actually occur. This allows correction of only partial errors rather than those which have been studied using Hamming distance, in non-binary cases. The paper considers a class of distances, SK-distances, in terms of which partial errors can be defined. Examining the sufficient condition for the existence of a parity check matrix for a given number of parity-checks, the paper contains an upper bound on the number of parity check digits for linear codes with property that corrects all partial random errors of an (n, k ) code with minimum SK-distance at least d. The result generalizes the rather widely used Varshamov-Gilbert bound, which follows from it as a particular case.

Upper Bound on Correcting Partial Random Errors

Department of Mathematics, JIIT, Noida, UP-201307, India

Cybernetics and Information Technologies

{"article-title":"Upper Bound on Correcting Partial Random Errors"}

Since coding has become a basic tool for practically all communication/electronic devices, it is important to carefully study the error patterns that actually...

Upper Bound on Correcting Partial Random Errors

Published Online: Sep 20, 2013

Page range: 41 - 49

DOI: https://doi.org/10.2478/cait-2013-0024

This content is open access.