Polar Decreasing Monomial-Cartesian Codes

In this article, we introduce a new family of polar codes from evaluation codes, called decreasing monomial-Cartesian and prove that families with multiple kernels over certain symmetric channels can be viewed as codes. This offers unified treatment for such any finite field. We define obtained set monomials closed under divisibility Cartesian product determine their parameters (length, dimension, minimum distance). show the dual code is monomially equivalent to code. Polar are then by utilizing whose sets respect partial order. sequence invertible matrices an arbitrary field satisfying conditions polarizes channel