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 = q(m)-1/lambda , where lambda | q - 1 and m >= 3 is odd. It is proved that there exist q-ary self-orthogonal cyclic codes with parameters [ n, n - 1/2 >= d] for even prime power q , and [ n, n - 1/2, >= d ] or [ n, n - 1/2, >= 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.