Generalizations and applications of the nowhere zero linear mappings in network coding |
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Authors: | Min Fang |
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Institution: | a Department of Mathematics, Tongji University, Shanghai 200092, PR China b The Center for Advanced Computer Studies, University of Louisiana at Lafayette, Lafayette, LA 70504, USA |
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Abstract: | In 2], Alon and Tarsi proposed a conjecture about the nowhere-zero point in linear mappings. In this paper, we first study some generalizations of this problem, and obtain necessary and sufficient conditions for the existence of nowhere point in these generalized problems under the assumption |F|?n+2, where n is the number of rows of the matrix A. Then we apply the results in these generalizations to give a polynomial time algebraic construction of the acyclic network codings. |
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Keywords: | 05B20 15A30 |
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