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      Correlations between the ranks of submatrices and weights of random codes

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      Author
      Klyachko, A. A.
      Özen, I.
      Date
      2009
      Source Title
      Finite Fields and Their Applications
      Print ISSN
      1071-5797
      Electronic ISSN
      1090-2465
      Volume
      15
      Issue
      4
      Pages
      497 - 516
      Language
      English
      Type
      Article
      Item Usage Stats
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      Abstract
      The 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.
      Keywords
      Classification of subspaces
      Cumulant
      Random codes
      Random matrices
      Rank
      Weight enumerator of a random code
      Classification of subspaces
      Cumulant
      Random codes
      Random matrices
      Rank
      Weight enumerator of a random code
      Matrix algebra
      Permalink
      http://hdl.handle.net/11693/22682
      Published Version (Please cite this version)
      http://dx.doi.org/10.1016/j.ffa.2009.03.002
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