On the Limit Distribution of the Number of Solutions of a Random System of Linear Equations in the Class of Boolean Functions
И. Н. Коваленко · Theory of Probability and Its Applications · 1967
Previous article Next article On the Limit Distribution of the Number of Solutions of a Random System of Linear Equations in the Class of Boolean FunctionsI. N. KovalenkoI. N. Kovalenkohttps://doi.org/10.1137/1112005PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] B. L. van der Waerden, Modern Algebra. Vol. I, Frederick Ungar Publishing Co., New York, N. Y., 1949xii+264, Part 2 MR0029363 0033.10102 Google Scholar[2] I. N. Kovalenko, A limit theorem for determinants in the class of Boolean functions, Dokl. Akad. Nauk SSSR, 161 (1965), 517–519, (In Russian.) MR0175164 Google Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails The rank of sparse random matricesRandom Structures & Algorithms, Vol. 195 | 23 April 2022 Cross Ref Distributed Decoding for Coded Slotted ALOHAIEEE Communications Letters, Vol. 21, No. 8 | 1 Aug 2017 Cross Ref Probabilistic bounds on the trapping redundancy of linear codes2016 IEEE International Symposium on Information Theory (ISIT) | 1 Jul 2016 Cross Ref Bounds on the expected rank of sparse linear operator channel matrices2013 19th Asia-Pacific Conference on Communications (APCC) | 1 Aug 2013 Cross Ref Kovalenko's full-rank limit and overheads as lower bounds of error-performances of LDPC and LT codes over binary erasure channels2008 International Symposium on Information Theory and Its Applications | 1 Dec 2008 Cross Ref Improved Probabilistic Bounds on Stopping RedundancyIEEE Transactions on Information Theory, Vol. 54, No. 4 | 1 Apr 2008 Cross Ref Smooth and sharp thresholds for random {k} -XOR-CNF satisfiabilityRAIRO - Theoretical Informatics and Applications, Vol. 37, No. 2 | 15 November 2003 Cross Ref An exactly solvable random satisfiability problemJournal of Physics A: Mathematical and General, Vol. 35, No. 36 | 30 August 2002 Cross Ref On the distribution of rank of a random matrix over a finite fieldRandom Structures and Algorithms, Vol. 17, No. 3-4 | 1 January 2000 Cross Ref Satisfiability threshold for random XOR-CNF formulasDiscrete Applied Mathematics, Vol. 96-97 | 1 Oct 1999 Cross Ref The Probability of Consistency of a System of Random Linear Equations over an Arbitrary Finite RingA. A. LevitskayaTheory of Probability & Its Applications, Vol. 30, No. 2 | 17 July 2006AbstractPDF (964 KB)Invariance theorems for the behavior in the limit of the number of solutions of a system of random linear equations over a finite ringCybernetics, Vol. 14, No. 2 | 1 Jan 1978 Cross Ref Invariance theorems for random Boolean matricesCybernetics, Vol. 11, No. 5 | 1 Jan 1976 Cross Ref A Limit Theorem for a Characteristic of a Random Boolean MatrixM. V. KozlovTheory of Probability & Its Applications, Vol. 16, No. 1 | 17 July 2006AbstractPDF (770 KB)The Distribution of the Rank of Random Matrices over a Finite FieldG. V. BalakinTheory of Probability & Its Applications, Vol. 13, No. 4 | 17 July 2006AbstractPDF (665 KB) Volume 12, Issue 1| 1967Theory of Probability & Its Applications1-157 History Submitted:25 February 1966Published online:17 July 2006 InformationCopyright © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1112005Article page range:pp. 47-56ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics