The Average Hull Dimension of Negacyclic Codes over Finite Fields

Hulls of linear codes have been extensively studied due to their wide applications and links with the efficiency of some algorithms in coding theory. In this paper, the average dimension of the Euclidean hull of negacyclic codes of length n over finite fields F-q, denoted by E (n, -1, q), has been investigated. The formula for E (n, -1, q) has been determined. Some upper and lower bounds of E (n, -1, q) have been given as well. Asymptotically, it has been shown that either E (n, -1, q) is zero or it grows the same rate as n.