Conflict-avoiding codes (CACs) have been used in multiple-access collision channel without feedback. The size of a CAC is the number of potential users that can be supported in the system. A code with maximum size is called optimal. The use of an optimal CAC enables the largest possible number of asynchronous users to transmit information efficiently and reliably. In this paper, a new upper bound on the maximum size of arbitrary equi-difference CAC is presented. Furthermore, three optimal constructions of equi-difference CACs are also given. One is a generalized construction for prime length $L=p$ and the other two are for two-prime length $L=pq$.

中文翻译：

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等权重上避免等差冲突码的新上限和最优构造

避免冲突代码（CAC）已在多路访问冲突通道中使用，没有反馈。CAC的大小是系统中可以支持的潜在用户数。具有最大大小的代码称为最优代码。最佳CAC的使用使尽可能多的异步用户可以有效而可靠地传输信息。在本文中，提出了一个新的任意等差CAC的最大大小的上限。此外，还给出了三种等差CAC的最佳构造。一个是素数长度$ L = p $的广义构造，另外两个是二素数长度$ L = pq $的广义构造。