基于 2 个不相交子集的 MDS 自对偶码构造

最大距离可分(maximum distance separable, MDS)自对偶码是一类最优线性码，在通信、数据存储和区组设计等领域有着广泛的应用，构造 MDS 自对偶码是当前编码理论研究的一个热点问题。文章基于有限域及其乘法群的 2 个不相交子集，利用广义 Reed-Solomon(RS)码构造了几类新的 MDS 自对偶码；得到的 MDS 自对偶码具有灵活的长度。

Maximum distance separable (MDS) self-dual codes are a class of optimal linear codes, which can be extensively applied in many fields such as communications, data storage and block designs. It has become a hot topic to construct MDS self-dual codes in coding theory. In this paper, several new classes of MDS self-dual codes are constructed from generalized Reed-Solomon (RS) codes based on two disjoint subsets of the multiplicative subgroup of a finite field. The resulting MDS self-dual codes have flexible lengths.