Rastsal kodlar ve matrisler

Results of our study are two fold. From the code theoretical point of view ourstudy yields the expectations and the covariances of the coe±cients of the weightenumerator of a random code. Particularly interesting is that, the coe±cients ofthe weight enumerator of a code with random parity check matrix are uncorre-lated. We give conjectures for the triple correlations of the coe±cients of weightenumerator of random codes. From the random matrix theory point of view weobtain results in the rank distribution of column submatrices. We give the ex-pectations and the covariances between the ranks (q¡rank) of such submatricesover Fq. We conjecture the counterparts of these results for arbitrary subma-trices. The case of higher correlations gets drastically complicated even in thecase of three submatrices. We give a formula for the correlation of ranks of threesubmatrices and a conjecture for its closed form.