On Binary LCD Cyclic Codes

Abstract

A binary linear code C is called a linear complementary dual (LCD) code if it meets its dual trivially. The concept of strong coset leader is introduced to characterize LCD cyclic codes and a unified formula on the amount of LCD cyclic codes with given code length n is presented. Through a detailed analysis into the properties of 2-cyclotomic cosets, conditions of existence for nontrivial LCD cyclic codes are also given. Based on these results, LCD cyclic codes of odd length n ≤ 257 are investigated and many new LCD cyclic codes with very good parameters are presented.