2018/09/25 by Derong Xie, Xie, Derong, Jinquan Luo +1
Computer Science · Engineering · #Coding theory and cryptography #Cooperative Communication and Network Coding #FOS: Computer and information sciences #Information Theory (cs.IT) #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.1809.09300
openalex publication_date 2018/09/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
An equi-differece conflict-avoiding code (CACe) C of length n and weight ω is a collection of ω-subsets (called codewords) which has the form \0,i,2i,⋯,(ω-1)i\ of ℤn such that Δ(c1)∩Δ(c2)=∅ holds for any c1, c2\inC, c1≠ c2 where Δ(c)=\j-i (mod n) | i,j∈ c,i≠ j\. A code C∈ CACes with maximum code size for given n and ω is called optimal and is said to be perfect if ∪c∈ CΔ(c)=ℤn\backslash \0\. In this paper, we show how to combine a C1∈ CACe(q1,ω) and a C2∈ CACe(q2,ω) into a C∈ CACe(q1q2,ω) under certain conditions. One necessary condition for a CACe of length q1q2 and weight ω being optimal is given. We also consider explicit construction of perfect C∈ CACe(p,ω) of odd prime p and weight ω≥3. Finally, for positive integer k and prime p≡1 (mod 4k), we consider explicit construction of quasi-perfect C∈ CACe(2p,4k+1).