NDLI: Stopping Set Distributions of Some Linear Codes

Content Provider	IEEE Xplore Digital Library
Author	Shu-Tao Xia Fang-Wei Fu
Copyright Year	2006
Description	Author affiliation: Graduate Sch. at Shenzhen, Tsinghua Univ., Beijing (Shu-Tao Xia)
Abstract	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 $\\^{T_{i}(H)\\^}^{n}$ $_{i=0}$ 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 determined with explicit formula. With parity-check matrix formed by all the nonzero codewords of the simplex code, the SSD of the Hamming code is completely determined with two recursive equations. Then, the first order Reed-Muller codes and the extended Hamming codes are discussed. With parity-check matrix formed by all the weight 4 codewords of the extended Hamming code, the SSD of the first order Reed-Muller code is completely determined with explicit formula. With parity-check matrix formed by all the minimum codewords of the first order Reed-Muller code, the SSD of the extended Hamming code is completely determined with two recursive equations
Starting Page	47
Ending Page	51
File Size	5887496
Page Count	5
File Format	PDF
ISBN	1424400678
DOI	10.1109/ITW2.2006.323751
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2006-10-22
Publisher Place	Uruguay
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Linear code Information geometry Conferences Laboratories H infinity control Parity check codes Iterative decoding Equations Information theory Maximum likelihood decoding
Content Type	Text
Resource Type	Article

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