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 <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> (H)} <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sup> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i=0</sub> 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
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
