Self-orthogonal cyclic codes with good parameters

The construction of self-orthogonal codes is an interesting topic due to their wide applications in communication and cryptography. In this paper, we construct several families of self-orthogonal cyclic codes with length $n=\frac{q^m-1}{\lambda }$, where $\lambda |q-1$ and $m\ge 3$ is odd. It is proved that there exist q-ary self-orthogonal cyclic codes with parameters $[n,\frac{n-1}{2},\ge d]$ for even prime power q, and $[n,\frac{n}{2}-1,\ge d]$ or $[n,\frac{n-1}{2},\ge d]$ for odd prime power q, where d is significantly better than the square-root bound. These several families of self-orthogonal cyclic codes contain some optimal linear codes.