2017/09/06 by Joydeb Pal, Pal, Joydeb, Pramod Kumar Maurya +5
Computer Science · Mathematics · #FOS: Computer and information sciences #Information Theory (cs.IT) #cs.IT #math.IT
paper · pdf · doi:10.48550/arxiv.1709.01825
arxiv created 2017/09/07 · arxiv updated 2017/09/08
An important code of length n2 is obtained by taking centralizer of a square matrix over a finite field \mathbbFq. Twisted centralizer codes, twisted by an element a ∈ \mathbbFq, 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):= \lbrace B ∈ \mathbbFqn × n|AB=BAD \rbrace 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 n2 by construction but in this paper, we have constructed centralizer codes of length (n2-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.