Abstract
The problem to construct optimal conflict-avoiding codes of even lengths and the Hamming weight 3 is completely settled. On the contrary, it is still open for odd lengths. It turns out that the prime lengths are the fundamental cases needed to be constructed. In the article, we study conflict-avoiding codes of prime lengths and give a connection with the so-called cyclotomic numbers. By having some nonzero cyclotomic numbers, a well-known algorithm for constructing optimal conflict-avoiding codes will work for certain prime lengths. As a consequence, we are able to answer the size of optimal conflict-avoiding code for a new class of prime lengths.
| Original language | English |
|---|---|
| Pages (from-to) | 6834-6841 |
| Number of pages | 8 |
| Journal | IEEE Transactions on Information Theory |
| Volume | 70 |
| Issue number | 10 |
| DOIs | |
| Publication status | Published - 2024 |
Keywords
- Binary protocol sequence
- cyclotomic matrices
- cyclotomic numbers
- multiple-access collision channel without feedback
- optimal conflict-avoiding code
- squares
ASJC Scopus subject areas
- Information Systems
- Computer Science Applications
- Library and Information Sciences