学术报告报告主题：New Constructions of Optimal Cyclic $(r, \delta)$ Locally Repairable
Codes from Their Zeros
报 告人：郑大彬 教授 (湖北大学)
报告地点：腾讯会议，会议号167 584 376
报告时间：2022年3月27日(星期日)，15：20-16：10。
邀 请人：陈博聪 教授
欢迎广大师生前往！
数学学院
2022年3月25日
报告摘要：An $(r, \delta)$-locally repairable code ($(r, \delta)$-LRC for short) was introduced by Prakash et al. for tolerating multiple failed nodes in distributed storage systems, which was a generalization of the concept of $r$-LRCs produced by Gopalan et al.. An $(r, \delta)$-LRC is said to be optimal if it achieves the Singleton-like bound. Recently, Chen et al.[1] generalized the construction of cyclic $r$-LRCs proposed by Tamo et al.[3,4] and constructed several classes of optimal $(r, \delta)$-LRCs of length $n$ for $n | (q-1)$ or $n | (q+1)$, respectively in terms of a union of the set of zeros controlling the minimum distance and the set of zeros ensuring the locality. Following the work of [1,2], this paper first characterizes $(r, \delta)$-locality of a cyclic code via its zeros. Then we construct several classes of optimal cyclic $(r, \delta)$-LRCs of length $n$ for $n | (q-1)$ or $n | (q+1)$, respectively from the product of two sets of zeros. Our constructions include all optimal cyclic $(r,\delta)$-LRCs proposed in [1, 2], and our method seems more convenient to obtain optimal cyclic $(r, \delta)$-LRCs with flexible parameters. Moreover, many optimal cyclic $(r,\delta)$-LRCs of length $n$ for $n | (q-1)$ or $n | (q+1)$, respectively such that $(r+\delta-1)\nmid n$ can be obtained from our method.
[1] B. Chen, S. Xia, J. Hao, F. Fu, Constructions of optimal cyclic (r,\delta ) locally repairable codes, IEEE Trans. Inform. Theory, 64(4): 2499-2511, 2018.
[2] B. Chen, W. Fang, S. Xia, F. Fu, Constructions of optimal $(r,\delta)$ locally repairable codes via constacyclic codes, IEEE Trans. Communications, 67(8): 5253-5263, 2019.
[3] I. Tamo, A. Barg, S. Goparaju, R. Calderbank, Cyclic LRC codes and their subfield subcodes, 2015 IEEE Int.Symp. Inform. Theory (ISIT), Hong Kong, 1262-1266, 2015.
[4] I. Tamo, A. Barg, S. Goparaju, R. Calderbank, Cyclic LRC codes, binary LRC codes, and upper bounds on the distance of cyclic codes, Int. J. Inf. Coding Theory, 3(4): 345-364, 2016.
报告人简介：郑大彬，湖北大学教授、博士生导师、副院长，中国数学会理事、中国工业与应用数学学会编码密码及相关组合理论专委会委员、中国数学会计算机数学专业委员会委员、湖北省数学会理事。2006年于中科院数学与系统科学研究院获博士学位，2009年6月至2012年4月在中科院研究生院信息安全国家重点实验室从事博士后研究工作，2015年3月至2016年2月在美国特拉华大学访问、学习。研究方向为编码学、密码学。主持国家重点研发计划子课题1项、国家自然科学基金项目3项和省部级项目多项。在《IEEE Transactions on Information Theory》、《Design, Codes and Cryptography》、《Finite Fields and Their Applications》、《Discrete Mathematics》、《Cryptography and Communications》、《Science China Mathematics》等国内外重要学术刊物和国际会议上发表论文40余篇。曾获得第31届国际符号与代数计算(ISSAC2006)年会杰出论文奖。