Almost disjunctive list-decoding codes

Abstract. A binary code is said to be a disjunctive list-decoding sL-code, s ≥ 1, L ≥ 1, (briefly, LD sL-code) if the code is identified by the incidence matrix of a family of finite sets in which the union of any s sets can cover not more than L− 1 other sets of the family. In this paper, we introduce a natural probabilistic generalization of LD sL-code when the code is said to be an almost disjunctive LD sL-code if the unions of almost all s sets satisfy the given condition. We develop a random coding method based on the ensemble of binary constant-weight codes to obtain lower bounds on the capacity and error probability exponent of such codes. For the considered ensemble our lower bounds are asymptotically tight.