Upper bounds for Turán numbers
Journal of Combinatorial Theory Series A
Concrete Math
Generic erasure correcting sets: bounds and constructions
Journal of Combinatorial Theory Series A - Special issue in honor of Jacobus H. van Lint
Low-density parity-check codes based on finite geometries: a rediscovery and new results
IEEE Transactions on Information Theory
Finite-length analysis of low-density parity-check codes on the binary erasure channel
IEEE Transactions on Information Theory
On the stopping distance and the stopping redundancy of codes
IEEE Transactions on Information Theory
On the Stopping Redundancy of Reed–Muller Codes
IEEE Transactions on Information Theory
Improved Upper Bounds on Stopping Redundancy
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Pseudocodewords of Tanner Graphs
IEEE Transactions on Information Theory
Results on Parity-Check Matrices With Optimal Stopping And/Or Dead-End Set Enumerators
IEEE Transactions on Information Theory
Improved Probabilistic Bounds on Stopping Redundancy
IEEE Transactions on Information Theory
Stopping set distributions of algebraic geometry codes from elliptic curves
TAMC'12 Proceedings of the 9th Annual international conference on Theory and Applications of Models of Computation
Hi-index | 754.84 |
For a linear block code C, its stopping redundancy is defined as the smallest number of check nodes in a Tanner graph for C, such that there exist no stopping sets of size smaller than the minimum distance of C. Schwartz and Vardy conjectured that the stopping redundancy of a maximum-distance separable (MDS) code should only depend on its length and minimum distance. We define the (n, t)-single-exclusion number, S(n, t) as the smallest number of t-subsets of an n-set, such that for each i-subset of the i-set, i = 1, ..., t + 1, there exists a t-subset that contains all but one element of the i-subset. New upper bounds on the single-exclusion number are obtained via probabilistic methods, recurrent inequalities, as well as explicit constructions. The new bounds are used to better understand the stopping redundancy of MDS codes. In particular, it is shown that for [n, k = n - d + 1, d] MDS codes, as n → ∞, the stopping redundancy is asymptotic to S(n, d - 2), if d = o(√n), or if k = o(√n), k → ∞, thus giving partial confirmation of the Schwartz-Vardy conjecture in the asymptotic sense.