In this paper, we focus on the design of binary constant weight codes that admit low-complexity encoding and decoding algorithms, and that have size M=2k\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{w...
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In this paper, we focus on the design of binary constant weight codes that admit low-complexity encoding and decoding algorithms, and that have size M=2k\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$M=2<^>k$$\end{document} so that codewords can conveniently be labeled with binary vectors of length k. For every integer & ell;>= 3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\ell \ge 3$$\end{document}, we construct a (n=2 & ell;,M=2k & ell;,d=2)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(n=2<^>\ell , M=2<^>{k_{\ell }}, d=2)$$\end{document} constant weight code C[& ell;]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{{\mathcal {C}}}}[\ell ]$$\end{document} of weight & ell;\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\ell $$\end{document} by encoding information in the gaps between successive 1's of a vector, and call them as cyclic-gap constant weight codes. The code is associated with a finite integer sequence of length & ell;\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \us
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