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On the construction of bent functions of $n+2$ variables from bent functions of $n$ variables
Weight distribution and decoding of codes on hypergraphs
| 1. | Dept. of ECE and Institute for Systems Research, University of Maryland, College Park, MD 20742 |
| 2. | Department of Electrical and Computer Engineering, University of Maryland, College Park, MD 20742, United States |
| 3. | Institut de Mathématiques de Bordeaux, Université de Bordeaux 1, 351 cours de la Libération, 33405 Talence, France |
In this paper we study two aspects of hypergraph codes. First, we compute the weight enumerators of several ensembles of such codes, establishing conditions under which they attain the Gilbert-Varshamov bound and deriving estimates of their distance. In particular, we show that this bound is attained by codes constructed on a fixed bipartite graph with a large spectral gap.
We also suggest a new decoding algorithm of hypergraph codes that corrects a constant fraction of errors, improving upon the algorithm of Bilu and Hoory.
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2020 Impact Factor: 0.935
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