题目：A Sphere-Packing Bound for Locally Repairable Codes

报告人: 张志芳  副研究员 （中国科学院数学与系统科学研究院）

Abstract: For locally repairable codes (LRCs), V. Cadambe and A. Mazumdar derived the first field-dependent parameter bound, known as the C-M bound. However, the C-M bound depends on an undetermined parameter k(q)opt(n,d). In this paper, a sphere-packing approach is developed for upper bounding the parameter k for [n,k,d] linear LRCs with locality r. More specifically, three explicit bounds (Bound A,B,C) are derived. Bound A holds under the hypothesis that the local repair groups are disjoint and of equal size. Comparing with previous bounds obtained under the same hypothesis, Bound A either subsumes them as special cases or has an advantage due to its explicit form. Then the hypothesis is removed in Bound B and Bound C. As the price for explicit form, Bound B specially holds for d>=5 and Bound C for r=2. Through specific comparisons we show that Bound B and Bound C both tend to outperform the C-M bound as n goes large. Lastly, all the bounds are extended to q-ary LRCs.

时间：9月13日（星期四）下午4:30-5:30

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