2014/10/30 by A.G. D'yachkov, Arkadii D'yachkov, D'yachkov, Arkadii +7
Computer Science · Engineering · Mathematics · #Coding theory and cryptography #Cooperative Communication and Network Coding #FOS: Computer and information sciences #Information Theory (cs.IT) #cs.IT #graph theory and CDMA systems #math.IT
paper · pdf · doi:10.48550/arxiv.1410.8385
18 pages, 1 figure, 1 table, conference paper
openalex publication_date 2014/10/30 · arxiv created 2015/03/29 · arxiv updated 2015/03/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A binary code is said to be a disjunctive list-decoding sL-code (LD sL-code), s ≥ 2, L ≥ 1, if the code is identified by the incidence matrix of a family of finite sets in which the union (or disjunctive sum) of any s sets can cover not more than L-1 other sets of the family. In this paper, we consider a similar class of binary codes which are based on a \em symmetric disjunctive sum (SDS) of binary symbols. By definition, the symmetric disjunctive sum (SDS) takes values from the ternary alphabet \0, 1, *\, where the symbol~* denotes "erasure". Namely: SDS is equal to 0 (1) if all its binary symbols are equal to 0 (1), otherwise SDS is equal to~*. List decoding codes for symmetric disjunctive sum are said to be \em symmetric disjunctive list-decoding sL-codes (SLD sL-codes). In the given paper, we remind some applications of SLD sL-codes which motivate the concept of symmetric disjunctive sum. We refine the known relations between parameters of LD sL-codes and SLD sL-codes. For the ensemble of binary constant-weight codes we develop a random coding method to obtain lower bounds on the rate of these codes. Our lower bounds improve the known random coding bounds obtained up to now using the ensemble with independent symbols of codewords.