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

IF 0.3 Q4 MATHEMATICS
K. Ouahada, H. C. Ferreira
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引用次数: 1

Abstract

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.
新的距离概念和图论方法用于某些编码技术的设计与分析
摘要为某些编码技术引入的一个新的图距离概念有助于它们的设计和分析,例如在距离保持映射和谱整形码的情况下。一个图论构造,将二进制序列映射到置换序列,并受到k-立方体图的启发,已经达到了置换序列长度的某些值的距离和的上界。k立方体图中新引入的距离概念有助于首次更好地理解和分析距离约简映射的概念。距离和索引置换图概念的结合有助于揭示和验证谱零码的某些性质,这些性质以前很难分析。
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来源期刊
CiteScore
1.30
自引率
0.00%
发文量
3
审稿时长
16 weeks
期刊介绍: Communications in Applied and Industrial Mathematics (CAIM) is one of the official journals of the Italian Society for Applied and Industrial Mathematics (SIMAI). Providing immediate open access to original, unpublished high quality contributions, CAIM is devoted to timely report on ongoing original research work, new interdisciplinary subjects, and new developments. The journal focuses on the applications of mathematics to the solution of problems in industry, technology, environment, cultural heritage, and natural sciences, with a special emphasis on new and interesting mathematical ideas relevant to these fields of application . Encouraging novel cross-disciplinary approaches to mathematical research, CAIM aims to provide an ideal platform for scientists who cooperate in different fields including pure and applied mathematics, computer science, engineering, physics, chemistry, biology, medicine and to link scientist with professionals active in industry, research centres, academia or in the public sector. Coverage includes research articles describing new analytical or numerical methods, descriptions of modelling approaches, simulations for more accurate predictions or experimental observations of complex phenomena, verification/validation of numerical and experimental methods; invited or submitted reviews and perspectives concerning mathematical techniques in relation to applications, and and fields in which new problems have arisen for which mathematical models and techniques are not yet available.
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