On the characteristic roots and heart of a class of rhotrices over a finite field

Abstract

Matrices play an important role in various branches of mathematics such as coding theory, combinatorics and cryptography. Rhotrices are represented by coupled matrices. The use of rhotrices in cryptography doubles the security of messages which travel over insecure channels. We consider rhotrices of 3-dimension and derive some properties related to their characteristic roots. Further, we take a special class of rhotrices of $n$-dimension and discuss its properties.