Xiuling Shan

Yi Fu, Xiuling Shan

A linear code is referred to as a locally repairable code (LRC) with locality r if any erased code symbol can be recovered by accessing at most r other code symbols. LRCs are highly desirable for distributed storage systems to enhance repair efficiency. In this paper, we investigate LRCs with disjoint repair sets via the parity-check matrix method. Firstly, we propose a novel concept of the s-Pasch configuration and present a geometric characterization for the existence of LRCs with minimum distance 5 and locality 3. Subsequently, we construct k-optimal LRCs by exploiting the point-line relationship in PG(2,q). Finally, a family of q-ary k-optimal LRCs with minimum distance 6 and general locality r is constructed using partial r-spreads.

Honglian Shen, Xiuling Shan, Zihong Tian

There are some good combinatorial structures suitable for image encryption. In this study, a new chaotic image encryption algorithm based on transversals in a Latin square is proposed. By means of an n-transversal of a Latin square, we can permutate an image data group by group for the first time, then use two Latin squares for auxiliary diffusion on the basis of a chaotic sequence, finally make use of a pair of orthogonal Latin squares to do the second scrambling. As a whole, the encryption process of "scrambling-diffusion-scrambling" is formed. The experimental results indicate that this algorithm achieves a secure and fast encryption effect. The final information entropy is very close to 8, and the correlation coefficient is approximate to 0. All these tests verify the robustness and practicability of this proposed algorithm.