Refined upper bounds on stopping redundancy of binary linear codes
Yauhen Yakimenka, Vitaly Skachek · 2015
The l-th stopping redundancy ρι(C) of the binary [n, k, d] code C, 1 ≤ l ≤ d, is defined as the minimum number of rows in the parity-check matrix of C, such that the smallest stopping set is of size at least l. The stopping redundancy ρ(C) is defined as ρd(C). In this work, we improve on the probabilistic analysis of stopping redundancy, proposed by Han, Siegel and Vardy, which yields the best bounds known today. In our approach, we judiciously select the first few rows in the parity-check matrix, and then continue with the probabilistic method. By using similar techniques, we improve also on the best known bounds on ρι(C), for 1 ≤ l ≤ d. Our approach is compared to the existing methods by numerical computations.