<abstract xmlns="http://www.w3.org/1999/xhtml"><p>A New graph distance concept introduced for certain coding techniques helped in their design and analysis as in the case of distance-preserving mappings and spectral shaping codes. A graph theoretic construction, mapping binary sequences to permutation sequences and inspired from the <italic>k</italic>-cube graph has reached the upper bound on the sum of the distances for certain values of the length of the permutation sequence. The new introduced distance concept in the <italic>k</italic>-cube graph helped better understanding and analyzing for the first time the concept of distance-reducing mappings. A combination of distance and the index-permutation graph concepts helped uncover and verify certain properties of spectral null codes, which were previously difficult to analyze.</p></abstract>

A New graph distance concept introduced for certain coding techniques helped in their design and analysis as in the case of distance-preserving mappings and spectral shaping codes. A graph theoretic construction, mapping binary sequences to permutation sequences and inspired from the k-cube graph has reached the upper bound on the sum of the distances for certain values of the length of the permutation sequence. The new introduced distance concept in the k-cube graph helped better understanding and analyzing for the first time the concept of distance-reducing mappings. A combination of distance and the index-permutation graph concepts helped uncover and verify certain properties of spectral null codes, which were previously difficult to analyze.

New Distance Concept and Graph Theory Approach for Certain Coding Techniques Design and Analysis

Department of Electrical and Electronic Engineering Science

Communications in Applied and Industrial Mathematics

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

A New graph distance concept introduced for certain coding techniques helped in their design and analysis as in the case of distance-preserving mappings and...

New Distance Concept and Graph Theory Approach for Certain Coding Techniques Design and Analysis

Published Online: May 11, 2019

Page range: 53 - 70

Received: May 21, 2017

Accepted: Mar 28, 2019

DOI: https://doi.org/10.1515/caim-2019-0012

Keywords
Graph theory, Distance mappings, Spectral codes, Cube graph, index permutation graph

© 2019 Khmaies Ouahada et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

New Distance Concept and Graph Theory Approach for Certain Coding Techniques Design and Analysis

Published Online: May 11, 2019

Page range: 53 - 70

Received: May 21, 2017

Accepted: Mar 28, 2019

DOI: https://doi.org/10.1515/caim-2019-0012

KeywordsGraph theory, Distance mappings, Spectral codes, Cube graph, index permutation graph

© 2019 Khmaies Ouahada et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
Graph theory, Distance mappings, Spectral codes, Cube graph, index permutation graph