# Stopping Set Distributions of Some Linear Codes

```@article{Jiang2006StoppingSD,
title={Stopping Set Distributions of Some Linear Codes},
author={Yong Jiang and Shutao Xia and Fangwei Fu},
journal={2006 IEEE Information Theory Workshop - ITW '06 Chengdu},
year={2006},
pages={47-51}
}```
• Published 1 October 2006
• Computer Science
• 2006 IEEE Information Theory Workshop - ITW '06 Chengdu
In this paper, the stopping set distributions (SSD) of some well-known binary linear codes are determined by using finite geometry theory. Similar to the weight distribution of a binary linear code, the SSD {Ti(H)}n i=0 enumerates the number of stopping sets with size i of a linear code with parity-check matrix H. First, we deal with the simplex codes and Hamming codes. With parity-check matrix formed by all the weight 3 codewords of the Hamming code, the SSD of the simplex code is completely…
6 Citations
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• Computer Science, Mathematics
IEEE Transactions on Information Theory
• 2014
The stopping sets, the stopping set distribution, and the stopping distance of the AG code from an elliptic Curve are reduced to the search, counting, and decision versions of the subset sum problem in the group of rational points of the elliptic curve, respectively.
Stopping Set Distributions of Algebraic Geometry Codes from Elliptic Curves
• Computer Science, Mathematics
TAMC
• 2012
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 and the group structure of rational points of elliptic curves is used to present a complete characterization of stopping sets.
Stopping Set Distributions of Some Reed–Muller Codes
• Computer Science
IEEE Transactions on Information Theory
• 2011
Finite geometry in combinatorics is used to obtain BEC-optimal parity-check matrices and then determine the stopping set distributions for the Simplex codes, the Hamming code, the first order Reed-Muller codes, and the extended Hamming codes, which are some Reed-muller Codes or their shortening or puncturing versions.
Generalized Stopping Sets and Stopping Redundancy
• Computer Science
2007 Information Theory and Applications Workshop
• 2007
A general iterative decoding technique that gives a more refined trade-off between complexity and performance, and basic properties and examples of both generalized stopping sets and generalized stopping redundancy are presented.
Generalized Iterative Decoding for Linear Block Codes on the Binary Erasure Channel
• Computer Science
2007 IEEE International Symposium on Information Theory
• 2007
This paper considers aspects regarding the implementation of generalized iterative decoding and determines the minimum order (as a function of the girth) that can potentially lead to improvement over traditional iterative decode.
On the minimum stopping sets of product codes
• Computer Science
• 2018
It is shown that the certain combinatorial structures called stopping sets have the important role in analysis of iterative decoding and the number of minimum stopping sets of the corresponding component codes is determined.

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