Bounds and Constructions for 3-Separable Codes with Length 3 [article]

Minquan Cheng, Jing Jiang, Haiyan Li, Ying Miao, Xiaohu Tang
2015 arXiv   pre-print
Separable codes were introduced to provide protection against illegal redistribution of copyrighted multimedia material. Let C be a code of length n over an alphabet of q letters. The descendant code desc(C_0) of C_0 = { c_1, c_2, ..., c_t}⊆C is defined to be the set of words x = (x_1, x_2, ...,x_n)^T such that x_i ∈{c_1,i, c_2,i, ..., c_t,i} for all i=1, ..., n, where c_j=(c_j,1,c_j,2,...,c_j,n)^T. C is a t-separable code if for any two distinct C_1, C_2 ⊆C with |C_1| < t, |C_2| < t, we always
more » ... have desc(C_1) ≠ desc(C_2). Let M(t,n,q) denote the maximal possible size of such a separable code. In this paper, an upper bound on M(3,3,q) is derived by considering an optimization problem related to a partial Latin square, and then two constructions for 3-SC(3,M,q)s are provided by means of perfect hash families and Steiner triple systems.
arXiv:1507.00954v1 fatcat:yoexz3slgze3ramzl3exrwzuxa