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In this paper, a criterion of MDS Euclidean self-orthogonal codes is presented. New MDS Euclidean self-dual codes and self-orthogonal codes are constructed via this criterion. In particular, among our constructions, for large square $q$, about $frac{1}{8}cdot q$ new MDS Euclidean (almost) self-dual codes over $F_q$ can be produced. Moreover, we can construct about $frac{1}{4}cdot q$ new MDS Euclidean self-orthogonal codes with different even lengths $n$ with dimension $frac{n}{2}-1$.
The parameters of MDS self-dual codes are completely determined by the code length. In this paper, we utilize generalized Reed-Solomon (GRS) codes and extended GRS codes to construct MDS self-dual (self-orthogonal) codes and MDS almost self-dual code
The parameters of a $q$-ary MDS Euclidean self-dual codes are completely determined by its length and the construction of MDS Euclidean self-dual codes with new length has been widely investigated in recent years. In this paper, we give a further stu
In this paper, we propose a mechanism on the constructions of MDS codes with arbitrary dimensions of Euclidean hulls. Precisely, we construct (extended) generalized Reed-Solomon(GRS) codes with assigned dimensions of Euclidean hulls from self-orthogo
Maximum distance separable (MDS) codes are optimal where the minimum distance cannot be improved for a given length and code size. Twisted Reed-Solomon codes over finite fields were introduced in 2017, which are generalization of Reed-Solomon codes.
In this paper, we produce new classes of MDS self-dual codes via (extended) generalized Reed-Solomon codes over finite fields of odd characteristic. Among our constructions, there are many MDS self-dual codes with new parameters which have never been