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Let $p$ be a prime and let $q$ be a power of $p$. In this paper, by using generalized Reed-Solomon (GRS for short) codes and extended GRS codes, we construct two new classes of quantum maximum-distance- separable (MDS) codes with parameters [ [[tq, tq-2d+2, d]]_{q} ] for any $1 leq t leq q, 2 leq d leq lfloor frac{tq+q-1}{q+1}rfloor+1$, and [ [[t(q+1)+2, t(q+1)-2d+4, d]]_{q} ] for any $1 leq t leq q-1, 2 leq d leq t+2$ with $(p,t,d) eq (2, q-1, q)$. Our quantum codes have flexible parameters, and have minimum distances larger than $frac{q}{2}+1$ when $t > frac{q}{2}$. Furthermore, it turns out that our constructions generalize and improve some previous results.
It is an important task to construct quantum maximum-distance-separable (MDS) codes with good parameters. In the present paper, we provide six new classes of q-ary quantum MDS codes by using generalized Reed-Solomon (GRS) codes and Hermitian construc
In this paper, we present three new classes of $q$-ary quantum MDS codes utilizing generalized Reed-Solomon codes satisfying Hermitian self-orthogonal property. Among our constructions, the minimum distance of some $q$-ary quantum MDS codes can be bi
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, 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{
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