Efficient Description of some Classes of Codes using Group Algebras. (arXiv:2208.04061v1 [cs.IT])

Circulant matrices are an important tool widely used in coding theory and
cryptography. A circulant matrix is a square matrix whose rows are the cyclic
shifts of the first row. Such a matrix can be efficiently stored in memory
because it is fully specified by its first row. The ring of $n \times n$
circulant matrices can be identified with the quotient ring
$\mathbb{F}[x]/(x^n-1)$. In consequence, the strong algebraic structure of the
ring $\mathbb{F}[x]/(x^n-1)$ can be used to study properties …