Cuiling Fan

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Linear codes with few weights have applications in secrete sharing, authentication codes, association schemes, and strongly regular graphs. In this paper, several classes of p-ary linear codes with two or three weights are constructed from quadratic Bent functions over the finite field F p , where p is an odd prime. They include some earlier linear codes as(More)
Reed-Solomon codes, a type of BCH codes, are widely employed in communication systems, storage devices and consumer electronics. This fact demonstrates the importance of BCH codes – a family of cyclic codes – in practice. In theory, BCH codes are among the best cyclic codes in terms of their error-correcting capability. A subclass of BCH codes are the(More)
We present unified constructions of optical orthogonal codes (OOCs) using other combinatorial objects such as cyclic linear codes and frequency hopping sequences. Some of obtained OOCs are optimal or asymptotically optimal with respect to the Johnson bound. Also, we are able to show the existence of new optimal frequency hopping sequences (FHSs) with(More)
Linear codes with few weights have applications in secrete sharing, authentication codes, association schemes, and strongly regular graphs. In this paper, a construction of q-ary linear codes with few weights employing general quadratic forms over the finite field F q ${\mathbb {F}}_{q}$ is proposed, where q is an odd prime power. This generalizes some(More)
Locally repairable codes are desirable for distributed storage systems to improve the repair efficiency. In this paper, we first build a bridge between locally repairable code and packing. As an application of this bridge, some optimal locally repairable codes can be obtained by packings, which gives optimal locally repairable codes with flexible parameters.
Cyclic codes are a subclass of linear codes and have applications in consumer electronics, data storage systems, and communication systems as they have efficient encoding and decoding algorithms. Let m = 2ℓ + 1 for an integer ℓ ≥ 1 and π be a generator of GF(3 m) *. In this paper, a class of cyclic codes C (u,v) over GF(3) with two nonzeros π u and π v is(More)