A note on the hull and linear complementary pair of cyclic codes

The Euclidean hull of a linear code C is defined as C boolean AND C-perpendicular to, where C-perpendicular to denotes the dual of C under the Euclidean inner product. A linear code with zero hull dimension is called a linear complementary dual (LCD) code. A pair (C,D) of linear codes of length n over F-q is called a linear complementary pair (LCP) of codes if C circle plus D = F-q(n). In this paper, we give a characterization of LCD and LCP of cyclic codes of length qm-1, m >= 1, over the finite field F-q in terms of their basic dual zeros and their trace representations. We also formulate the hull dimension of a cyclic code of arbitrary length over F-q with respect to its basic dual zero. Moreover, we provide a general formula for the dimension of the intersection of two cyclic codes of arbitrary length over F-q based on their basic dual zeros.