Chaoping Xing

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In coding theory, self-dual codes and cyclic codes are important classes of codes which have been extensively studied. The main objects of study in this paper are self-dual cyclic codes over finite fields, i.e., the intersection of these two classes. We show that self-dual cyclic codes of length <i>n</i> over \BBF<i>q</i> exist if and only if <i>n</i> is(More)
It is known that quantum error correction can be achieved using classical binary codes or additive codes over (see [2], [3], [9]). In [1] and [4], asymptotically good quantum codes from algebraic-geometry codes were constructed and, in [1], a bound on ( ) was computed from the Tsfasman–Vlăduţ–Zink bound of the theory of classical algebraic-geometry codes.(More)
In this paper, we first construct several classes of classical Hermitian self-orthogonal maximum distance separable (MDS) codes. Through these classical codes, we are able to obtain various quantum MDS codes. It turns out that many of our quantum codes are new in the sense that the parameters of our quantum codes cannot be obtained from all previous(More)
The stabilizer method for constructing a class of asymmetric quantum codes (AQC), called additive AQC, has been established by Aly In this paper, we present a new characterization of AQC, which generalizes a result of the symmetric case known previously. As an application of the characterization, we establish a relationship of AQC with classical(More)
We consider Reed-Solomon (RS) codes whose evaluation points belong to a subfield, and give a linear-algebraic list decoding algorithm that can correct a fraction of errors approaching the code distance, while pinning down the candidate messages to a well-structured affine space of dimension a constant factor smaller than the code dimension. By pre-coding(More)
It has been a great challenge to construct new quantum maximum-distance-separable (MDS) codes. In particular, it is very hard to construct the quantum MDS codes with relatively large minimum distance. So far, except for some sparse lengths, all known q-ary quantum MDS codes have minimum distance &#x2264;q/2 + 1. In this paper, we provide a construction of(More)