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

Speaker: Zohreh Aliabadi, Sabanci University

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

Date/Time: 24 May 2023 / 13:40 - 14:30 

Place: FENS G015 (Physical Only)

Abstract: The Euclidean hull of a linear code C is defined as C∩C^⊥, where C^⊥ 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 ⊕D =F_q^n.
In this talk,  a characterization of LCD and LCP of cyclic codes of length q^m  - 1,m ≥ 1, over the finite field F_q in terms of their basic dual zeros and their trace representations will be given. A formulation of the hull dimension of a cyclic code of arbitrary length over F_q with respect to its basic dual zero will be provided.
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.