报告题目：New Constructions of Optimal Cyclic (r,δ) Locally Repairable Codes from Their Zeros

报 告 人： 郑大彬  湖北大学教授

报告时间：2022年4月19日（周二）上午10:00-12:00

报告形式：腾讯会议  会议号：187 330 871

报告摘要：An (r,δ)-locally repairable code ((r,δ)-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,δ)-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,δ)-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,δ)-locality of a cyclic code via its zeros. Then we construct several classes of optimal cyclic (r,δ)-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,δ)-LRCs proposed in [1, 2], and our method seems more convenient to obtain optimal cyclic (r,δ)-LRCs with flexible parameters. Moreover, many optimal cyclic (r,δ)-LRCs of length n for n|q-1 or n|q+1, respectively such that (r+δ-1)∤n can be obtained from our method.

[1] B. Chen, S. Xia, J. Hao, F. Fu, Constructions of optimal cyclic (r,δ) 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,δ) 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，理学博士、现为湖北大学数学与统计学学院教授、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理论专业委员会委员、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5月在中科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项以及省部级项目多项。在《IEEE Transactions on Information Theory》、《Designs,Codes and Cryptography》、《Finite Fields and Their Applications》、《Discrete Mathematics》、《Cryptography and Communications》、《Science China Mathematics》等国内外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。