2015/12/24 by Yeow Meng Chee, Xiande Zhang, Chee, Yeow Meng +1
Computer Science · Engineering · #Coding theory and cryptography #graph theory and CDMA systems #Cooperative Communication and Network Coding
paper · pdf · doi:10.48550/arxiv.1512.07719
The Johnson-type upper bound on the maximum size of a code of length n, distance d=2w-1 and constant composition w is \lfloor\dfracnw1\rfloor, where w is the total weight and w1 is the largest component of w. Recently, Chee et al. proved that this upper bound can be achieved for all constant-composition codes of sufficiently large lengths. Let Nccc(w) be the smallest such length. The determination of Nccc(w) is trivial for binary codes. This paper provides a lower bound on Nccc(w), which is shown to be tight for all ternary and quaternary codes by giving new combinatorial constructions. Consequently, by refining method, we determine the values of Nccc(w) for all q-ary constant-composition codes provided that 3w1≥ w with finite possible exceptions.