题目: Improved Lower Bounds for Constant-Composition Codes
摘要: There is a close relationship between Sidon set and error correcting code.
In this talk, we give a new construction for constant-composition codes with techniques in additive number theory. It turns out that when $d=4$ and $5$ our bound improves the one by Ding (2008) substantially. Moreover, we provide a new connection between constant-composition codes and linear block codes with certain properties. It turns out that when $d\geq 6$ our new lower bound improves the previous one by Ding (2008) substantially.
题目:Improved Bounds and Optimal Constructions of Locally Repairable Codes
摘要:In this talk, we first of all derive an improved and general upper bound on the code length of Singleton-optimal LRCs with minimum distance d=5, 6. Secondly, we obtain a complete characterization for Singleton-optimal LRCs with r=2 and d=6. And then we construct three new Singleton-optimal LRCs with large code length via some special structures of projective plane. In the end, we employ the well-known line-point incidence matrix and Johnson bounds for constant weight codes to derive tighter upper bounds on the code length, and the maximal value of the length of Singleton-optimal LRCs for some specific q are also determined.
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