Finding Self-Dual Quasi-Cyclic Codes with Large Minimum Weight via Polynomial Matrices

In this paper, we search for a class of self-dual quasi-cyclic (QC) codes over binary field with large minimum weight. We employ generator polynomial matrices to specify a QC code because there is a condition for them to be a self-dual code. By combining factorization and Chinese remainder theorem, we efficiently search for these codes. Moreover, under certain conditions, we use a method of reciprocal polynomials to make them more efficient. We construct self-dual QC codes whose cycle length is 5, 7 and 9, and find them with the best minimum weight in each condition.