A class of quantum codes over finite fields

Soumak Biswas, Maheshanand Bhaintwal

Zhonghua Sun, Xinyue Liu, Shixin Zhu

Hermitian dual-containing codes are an important class of linear codes which have important applications in the construction of quantum codes. In this paper, two classes of Hermitian dual-containing almost MDS codes over finite fields are studied. By employing the Hermitian construction, a class of quantum codes with minimum distance [Formula: see text] and a class of quantum codes with minimum distance [Formula: see text] are constructed.

Keke Liu, Zesong Fei, Jingming Kuang

In this paper, we present three algebraic methods for constructing structured nonbinary LDPC codes over finite fields, among which the first method is based on the multiplicative inverses of nonzero elements in finite fields and gives a class of quasi-cyclic codes with girth 6, the second method gives a class of (3, rho) quasi-cyclic codes with girth 8, the third method gives a class of structured codes with cycles limited. The codes given in examples perform well over AWGN channel and have better performances or far lower computational complexities than the corresponding random Mackay codes or codes algebraically constructed by Shu Lin.

Xiusheng Liu, Hualu Liu

Jian Gao, Yongkang Wang

In this short paper, we consider the non-binary quantum codes construction from a class of linear codes, which are not self-orthogonal over finite fields. As the computational results, new quantum codes [[8, 0, ≥ 4]]3, [[8, 2, ≥ 3]]3, [[11, 1, ≥ 5]]3, [[10, 0, ≥ 5]]4, and [[16, 6, ≥ 4]]4are obtained.

Hao Song, Ruihu Li, Yang Liu +1 more