Bounds and constructions of optimal symbol-pair codes with constant pair-weight

Symbol-pair codes introduced by Cassuto and Blaum in 2010 are designed to protect against pair errors in symbol-pair read channels. This special channel structure is motivated by the limitations of the reading process in high density data storage systems, where it is no longer possible to read individual symbols. In this work, we study bounds and constructions of codes in symbol-pair metric. By using some combinatorial structures, we give constructions of optimal q-ary symbol-pair codes with constant pair-weight wp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$w_p$$\end{document} and pair-distance 2wp-1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$2w_p-1$$\end{document} for some length n, and some optimal q-ary codes with pair-weight wp=3,4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$w_p=3,4$$\end{document} for all pair-distance between 3 and 2wp-1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$2w_p-1$$\end{document}.