The construction of two classes of self-orthogonal cyclic codes

As a notable subclass of linear codes, self-orthogonal codes play a crucial role in communication systems and cryptographic protocols. In our paper, we obtain the new constructions for several classes of self-orthogonal codes with length $ n = q^m-1 $, where $ m = 2l_1 $ and $ l_1 = 1 $ or odd prime. For $ m = 2l_1 $, where $ l_1 $ is an odd prime, a class of self-orthogonal codes with parameters $ \left[n, \frac{n-\left(q^{\frac{m}{2}}+1\right)}{2}, \ge q^{\frac{m}{2}}+q^2+2\right] $ is constructed. For $ m = 2 $, another class of self-orthogonal codes with parameters $ \left[n,\frac{n-\left(q+1\right)}{2},\ge 2q\right] $ is constructed. Compared with the codes in the codetables, these constructed self-orthogonal codes include some optimal or best linear codes.