Correlations between the ranks of submatrices and weights of random codes

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dc.citation.epage516en_US
dc.citation.issueNumber4en_US
dc.citation.spage497en_US
dc.citation.volumeNumber15en_US
dc.contributor.authorKlyachko, A. A.en_US
dc.contributor.authorÖzen, I.en_US
dc.date.accessioned2016-02-08T10:03:21Z
dc.date.available2016-02-08T10:03:21Z
dc.date.issued2009en_US
dc.departmentDepartment of Mathematicsen_US
dc.description.abstractThe results of our study are twofold. From the random matrix theory point of view we obtain results on the rank distribution of column submatrices. We give the moments and the covariances between the ranks (q- rank) of such submatrices. We conjecture the counterparts of these results for arbitrary submatrices. The case of higher correlations gets drastically complicated even in the case of three submatrices. We give a formula for the correlation of ranks of three submatrices and a conjecture for its closed form. From the code theoretical point of view our study yields the covariances of the coefficients of the weight enumerator of a random code. Particularly interesting is that the coefficients of the weight enumerator of a code with random parity check matrix are uncorrelated. We give a conjecture for the triple correlations between the coefficients of the weight enumerator of a random code. © 2009 Elsevier Inc. All rights reserved.en_US
dc.description.provenanceMade available in DSpace on 2016-02-08T10:03:21Z (GMT). No. of bitstreams: 1 bilkent-research-paper.pdf: 70227 bytes, checksum: 26e812c6f5156f83f0e77b261a471b5a (MD5) Previous issue date: 2009en
dc.identifier.doi10.1016/j.ffa.2009.03.002en_US
dc.identifier.eissn1090-2465
dc.identifier.issn1071-5797
dc.identifier.urihttp://hdl.handle.net/11693/22682
dc.language.isoEnglishen_US
dc.relation.isversionofhttp://dx.doi.org/10.1016/j.ffa.2009.03.002en_US
dc.source.titleFinite Fields and Their Applicationsen_US
dc.subjectClassification of subspacesen_US
dc.subjectCumulanten_US
dc.subjectRandom codesen_US
dc.subjectRandom matricesen_US
dc.subjectRanken_US
dc.subjectWeight enumerator of a random codeen_US
dc.subjectClassification of subspacesen_US
dc.subjectCumulanten_US
dc.subjectRandom codesen_US
dc.subjectRandom matricesen_US
dc.subjectRanken_US
dc.subjectWeight enumerator of a random codeen_US
dc.subjectMatrix algebraen_US
dc.titleCorrelations between the ranks of submatrices and weights of random codesen_US
dc.typeArticleen_US

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