Correlations between the ranks of submatrices and weights of random codes

Klyachko A. A., ÖZEN İ.

FINITE FIELDS AND THEIR APPLICATIONS, cilt.15, sa.4, ss.497-516, 2009 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 15 Sayı: 4
  • Basım Tarihi: 2009
  • Doi Numarası: 10.1016/j.ffa.2009.03.002
  • Dergi Adı: FINITE FIELDS AND THEIR APPLICATIONS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.497-516
  • Anahtar Kelimeler: Random codes, Random matrices, Rank, Weight enumerator of a random code, Cumulant, Classification of subspaces
  • Marmara Üniversitesi Adresli: Hayır

Özet

The results of our study are twofold. From the random matrix theory point of view we obtain results oil 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. (C) 2009 Elsevier Inc. All rights reserved.