题 目：New Constructions of Optimal Cyclic (r,δ) Locally Repairable Codes from Their Zeros
主讲人：郑大彬
时 间：2022年06月09日09:00-10:00
地 址：腾讯会议ID：643-107-062
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.
主讲人简介：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。
邀请人：胡思煌
审核人：魏普文
