Nonsingular plane cubic curves over finite fields
Journal of Combinatorial Theory Series A
Generic erasure correcting sets: bounds and constructions
Journal of Combinatorial Theory Series A - Special issue in honor of Jacobus H. van Lint
Algebraic Function Fields and Codes
Algebraic Function Fields and Codes
A deterministic reduction for the gap minimum distance problem: [extended abstract]
Proceedings of the forty-first annual ACM symposium on Theory of computing
On the stopping distance of array code parity-check matrices
IEEE Transactions on Information Theory
Single-exclusion number and the stopping redundancy of MDS codes
IEEE Transactions on Information Theory
Counting subset sums of finite abelian groups
Journal of Combinatorial Theory Series A
The intractability of computing the minimum distance of a code
IEEE Transactions on Information Theory
Finite-length analysis of low-density parity-check codes on the binary erasure channel
IEEE Transactions on Information Theory
A recursive approach to low complexity codes
IEEE Transactions on Information Theory
Stopping set distribution of LDPC code ensembles
IEEE Transactions on Information Theory
Using linear programming to Decode Binary linear codes
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
Computing the Stopping Distance of a Tanner Graph Is NP-Hard
IEEE Transactions on Information Theory
Complete Enumeration of Stopping Sets of Full-Rank Parity-Check Matrices of Hamming Codes
IEEE Transactions on Information Theory
Hard Problems of Algebraic Geometry Codes
IEEE Transactions on Information Theory
Improved Probabilistic Bounds on Stopping Redundancy
IEEE Transactions on Information Theory
Average Stopping Set Weight Distributions of Redundant Random Ensembles
IEEE Transactions on Information Theory
Permutation Decoding and the Stopping Redundancy Hierarchy of Cyclic and Extended Cyclic Codes
IEEE Transactions on Information Theory
Stopping Set Distributions of Some Reed–Muller Codes
IEEE Transactions on Information Theory
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The stopping sets and stopping set distribution of a binary linear code play an important role in the iterative decoding of the linear code over a binary erasure channel. In this paper, we study stopping sets and stopping distributions of some residue algebraic geometry (AG) codes. For the simplest AG code, i.e., generalized Reed-Solomon code, it is easy to determine all the stopping sets. Then we consider AG codes from elliptic curves. We use the group structure of rational points of elliptic curves to present a complete characterization of stopping sets. Then the stopping sets, the stopping set distribution and the stopping distance of the AG code from an elliptic curve are reduced to the search, computing and decision versions of the subset sum problem in the group of rational points of the elliptic curve, respectively.