Quasi-cyclic codes as codes over rings of matrices (Q964418)

This paper considers quasi-cyclic codes as cyclic codes over a ring of matrices over \(\mathbb{F}_q\). One of the main results of this paper is to generalize the correspondence between linear recurring sequences over a finite field and cyclic codes to the case of linear recurring sequences over a ring of matrices. The existence of the exponent for a polynomial with matricial coefficients has been shown. The construction of new quasi-cyclic codes and self-dual Euclidean codes (and Hermitian over \(\mathbb{F}_4\)) has also been taken up. Such a construction permits to find new self-dual Euclidean codes with parameters \([28,14,9]\) over \(\mathbb{F}_4\).