摘要 : The construction of self-dual codes with large minimum distances has been an active topic in coding theory. The construction and classification of extremal self-dual codes over small fields are related to other fields of mathemati... 展开 The construction of self-dual codes with large minimum distances has been an active topic in coding theory. The construction and classification of extremal self-dual codes over small fields are related to other fields of mathematics, such as lattices and invariant theory as well as combinatorial $t$ -designs. It is well-known that $q$ -ary self-dual cyclic codes exist only when $q$ is an even prime power and $q$ -ary self-dual negacyclic codes exist for any odd prime power $q$ . In 2009 a family of binary self-dual cyclic codes with lengths $n_{i}$ and minimum distances $d_{i} \geq \frac {1}{2} \sqrt {n_{i}}$ , where $n_{i}$ goes to the infinity if $i$ goes to the infinity, was constructed. In this paper, we construct several families of $q$ -ary self-dual negacyclic codes of lengths $n$ with their minimum distances larger than or equal to $n^{\frac {1}{2}}$ for various lengths $n$ and any given odd prime power $q$ . When $q \in \{3,5\}$ and the length is small, the minimum distances of the constructed self-dual negacyclic codes are comparable with these self-dual codes with largest known minimum distances in the literature. 收起