Optimal equi-difference conflict-avoiding codes of weight four
Optimal equi-difference conflict-avoiding codes of weight four
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DOI：
10.1007/s10623-014-0030-x
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发表时间：
2014-12
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影响因子：
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通讯作者：
Yiling Lin;Miwako Mishima;Masakazu Jimbo
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文献类型：
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作者：
Yiling Lin;Miwako Mishima;Masakazu Jimbo
长度和重量的冲突避免码（CAC）被定义为模剩余环的子集族（称为码字），使得对于任何，其中。在长度和重量相同的CAC中，如果每个码字都具有以下形式，则称之为等差码。在长度和重量的CAC中，如果具有最大码字数，则称该码为最优。在这篇文章中，我们研究的大小和结构的最佳码的重量为4的等距差CAC使用适当定义的有向图。因此，也提供了几个系列的无穷多个最佳等差CAC。
A conflict-avoiding code (CAC) of lengthand weightis defined as a familyof-subsets (called codewords) of, the ring of residues modulo, such thatfor any, where. A codein CACs of lengthand weightis called an equi-difference code if every codewordhas the form. A codein CACs of lengthand weightis said to be optimal ifhas the maximum number of codewords. In this article, we investigate sizes and constructions of optimal codes in equi-difference CACs of weight four by using properly defined directed graphs. As a consequence, several series of infinite number of optimal equi-difference CACs are also provided.