Generalized twisted centralizer codes

An important code of length n is obtained by taking centralizer of a square matrix over a finite field Fq. Twisted centralizer codes, twisted by an element a ∈ Fq, are also similar type of codes but different in nature. The main results were embedded on dimension and minimum distance. In this paper, we have defined a new family of twisted centralizer codes namely generalized twisted centralizer (GTC) codes by C(A,D) := {B ∈ F q |AB = BAD} twisted by a matrix D and investigated results on dimension and minimum distance. Parity-check matrix and syndromes are also investigated. Length of the centralizer codes is n by construction but in this paper, we have constructed centralizer codes of length (n − i), where i is a positive integer. In twisted centralizer codes, minimum distance can be at most n when the field is binary whereas GTC codes can be constructed with minimum distance more than n.