Xiaoshan Kai

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Let <i>q</i> be an odd prime power. Based on classical negacyclic codes, we construct two classes of quantum maximum-distance-separable (MDS) codes with parameters [[<i>q</i><sup>2</sup>+1, <i>q</i><sup>2</sup>-2<i>d</i>+3, <i>d</i>]]<i>q</i> where <i>q</i> &#x2261; 1 (mod 4) and 2 &#x2264; <i>d</i> &#x2264; <i>q</i>+1 is even, and(More)
One central theme in quantum error-correction is to construct quantum codes that have a large minimum distance. Quantum maximal distance separable (MDS) codes are optimal in the sense they attain maximal minimum distance. Recently, constructing quantum MDS codes has received much attention and seems to become more and more difficult. In this paper, based on(More)
We investigate cyclic self-dual codes over $${\mathbb{F}_{2^{r}}}$$ . We give a decomposition of a repeated-root cyclic codes over $${\mathbb{F}_{p^{r}}}$$ . The decomposition is used to analyze cyclic self-dual codes over $${\mathbb{F}_{2^{r}}}$$ . We obtain a necessary and sufficient condition for the existence of nontrivial cyclic self-dual codes over(More)
Recently, symbol-pair codes are proposed to protect against pair errors in symbol-pair read channels. One main task in symbol-pair coding theory is to design codes with large minimum pair distance. Maximum distance separable (MDS) symbol-pair codes are optimal in the sense they attain maximal minimum pair distance. In this paper, based on constacyclic(More)
In this paper, we determine the structure of negacyclic codes of even length over the ring Z2a and their dual codes. Furthermore we study self-dual negacyclic codes of even length over Z2a . A necessary and sufficient condition for the existence of nontrivial selfdual negacyclic codes is given, and the number of the self-dual negacyclic codes for a given(More)
Constacyclic codes are an important class of linear codes in coding theory. Many optimal linear codes are directly derived from constacyclic codes. In this paper, (1 − uv)-constacyclic codes over the local ring Fp + uFp + vFp + uvFp are studied. It is proved that the image of a (1 − uv)constacyclic code of length n over Fp + uFp + vFp + uvFp under a Gray(More)