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Optimal Conflict-Avoiding Codes with Weight 3
傅恒霖 教授(台湾交通大学应用数学系教授兼校训导长)
2018-01-01 12:13  华东师范大学

学 术 报 告
(运筹控制组)
报告题目: Optimal Conflict-Avoiding Codes with Weight 3
报告人:傅恒霖 教授(台湾交通大学应用数学系教授兼校训导长)
时间:2010年10月23日(周六)上午11:00-11:50;
地点:闵行校区数学楼102会议室
摘要: For a subset $A$ of $\mathbb{Z}_n$, define the difference set of A to be the multiset $\Delta(A)=\{i-j (mod n):i,j\in A,i\neq j\}.$ A conflict-avoiding code (CAC) of length $n$ and weight $k$ is a collection $\mathcal{C}$ of $k$-subsets, called codewords, of $\mathbb{Z}_n$ such that $\Delta(A)\cap \Delta(B) =\varnothing for any A, B\in \mathcal{C} with A\neq B.$ Let CAC $(n,k)$ be the class of all the CACs of length $n$ and weight $k$. The maximum size of codes in CAC$(n,k)$ is denoted by $M(n,k)$, i.e., $M(n,k)=max \{|\mathcal{C}|: \mathcal{C}\in$ CAC$(n,k)\}.$ A code $\mathcal{C}\in$ CAC$(n,k)$ is said to be optimal if $|\mathcal{C}|=M(n,k).$ In this talk, we shall give an update report of what has been done on finding optimal conflict-avoiding codes with weight 3, i.e., determining $M(n,3)$.