Asymptotic Combinatorial Coding Theory
Asymptotic Combinatorial Coding Theory
Introduction to Coding Theory
Algebraic-Geometric Codes
Lie Groups and Lie Algebras
Moments of the support weight distribution of linear codes
Designs, Codes and Cryptography
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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^-^r^a^n^k) 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.