Stopping Set Distributions of Some Linear Codes
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)ni=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 paritycheck 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.
Shu-Tao Xia Fang-Wei Fu
The Graduate School at Shenzhen Tsinghua University Shenzhen, Guangdong 518055, China Temasek Laboratories National University of Singapore Singapore 117508, Singapore
国际会议
2006年IEEE信息理论国际会议(Proceedings of 2006 IEEE Information Theory Workshop ITW06)
成都
英文
47-51
2006-10-22（万方平台首次上网日期，不代表论文的发表时间）