A Note on Matroids, Codes and Information Theory
نویسندگان
چکیده
In this note we show that the height function of a lattice of flats of suitable classes of matroids satisfies the polymatroidal axioms. Moreover, we present a novel proof, by applying matroid theory, for the fact that the minimum distance of a graph-theoretic code C is the smallest number of edges among the edge sets of cycles of G, where G is the graph arising C. AMS Subject Classification: 81Q99
منابع مشابه
Notes on matroids and codes
The following expository article is intended to describe a correspondence between matroids and codes. The key results are that the weight enumerator of a code is a specialisation of the Tutte polynomial of the corresponding matroid, and that the MacWilliams relation between weight enumerators of a code and its dual can be obtained from matroid duality. It also provides a general introduction to...
متن کاملA New Approach for Knowledge Based Systems Reduction using Rough Sets Theory (RESEARCH NOTE)
Problem of knowledge analysis for decision support system is the most difficult task of information systems. This paper presents a new approach based on notions of mathematical theory of Rough Sets to solve this problem. Using these concepts a systematic approach has been developed to reduce the size of decision database and extract reduced rules set from vague and uncertain data. The method ha...
متن کاملStructural properties of fuzzy graphs
Matroids are important combinatorial structures and connect close-lywith graphs. Matroids and graphs were all generalized to fuzzysetting respectively. This paper tries to study connections betweenfuzzy matroids and fuzzy graphs. For a given fuzzy graph, we firstinduce a sequence of matroids from a sequence of crisp graph, i.e.,cuts of the fuzzy graph. A fuzzy matroid, named graph fuzzy matro...
متن کاملDeveloping Coping Strategies with the Threats to Mental Health and the Family Structure of the Oil Company's Satellite Staff: a focus on the third type of change
Purpose: The aim of this study was to develop a strategic model in relation to the factors threatening the mental health and family structure of satellite employees of the oil company with emphasis on the focus of the third type of change. Method: In this study, a qualitative approach and a grounded theory method were used. The statistical population included all satellite personnel of South Za...
متن کاملPolynomial aspects of codes, matroids and permutation groups
Index 74 Preface The three subjects of the title (codes, matroids, and permutation groups) have many interconnections. In particular, in each case, there is a polynomial which captures a lot of information about the structure: we have the weight enumerator of a code, the Tutte polynomial (or rank polynomial) of a matroid, and the cycle index of a permutation group. With any code is associated a...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2011