TY - JOUR
T1 - Optimal tight equi-difference conflict-avoiding codes of length n = 2 k ± 1 and weight 3
AU - Wu, Shung Liang
AU - Fu, Hung-Lin
PY - 2013/6/1
Y1 - 2013/6/1
N2 - For a k-subset X of Zn, the set of differences on X is the set ΔX={i-j (mod n): i,jεX,i≠j}. A conflict-avoiding code CAC of length n and weight k is a collection C of k-subsets of Zn such that ΔXΔY = ø for any distinct X,YεC. 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). A code Cε CAC(n, k) is said to be optimal if |C| = M(n,k). An optimal code C is tight equi-difference if |CΔX = Zn\{0} and each codeword in C is of the form {0,i,2i,⋯,(k-1)i}. In this paper, the necessary and sufficient conditions for the existence problem of optimal tight equi-difference conflict-avoiding codes of length n = 2k±1 and weight 3 are given.
AB - For a k-subset X of Zn, the set of differences on X is the set ΔX={i-j (mod n): i,jεX,i≠j}. A conflict-avoiding code CAC of length n and weight k is a collection C of k-subsets of Zn such that ΔXΔY = ø for any distinct X,YεC. 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). A code Cε CAC(n, k) is said to be optimal if |C| = M(n,k). An optimal code C is tight equi-difference if |CΔX = Zn\{0} and each codeword in C is of the form {0,i,2i,⋯,(k-1)i}. In this paper, the necessary and sufficient conditions for the existence problem of optimal tight equi-difference conflict-avoiding codes of length n = 2k±1 and weight 3 are given.
KW - conflict-avoiding codes
KW - equi-difference
KW - optimal codes
UR - http://www.scopus.com/inward/record.url?scp=84875841867&partnerID=8YFLogxK
U2 - 10.1002/jcd.21332
DO - 10.1002/jcd.21332
M3 - Article
AN - SCOPUS:84875841867
VL - 21
SP - 223
EP - 231
JO - Journal of Combinatorial Designs
JF - Journal of Combinatorial Designs
SN - 1063-8539
IS - 6
ER -