2021-10-29
AUTHORSMinjia Shi, Shukai Wang, Xiaoxiao Li
ABSTRACTA code C is called ZpZp2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {Z}_p\mathbb {Z}_{p^2}$$\end{document}-linear if it is the Gray image of a ZpZp2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {Z}_p\mathbb {Z}_{p^2}$$\end{document}-additive code, where p>2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p>2$$\end{document} is prime. In this paper, the rank and the dimension of the kernel of ZpZp2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {Z}_p\mathbb {Z}_{p^2}$$\end{document}-linear codes are studied. The range of their values is given. For each value of the rank of ZpZp2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {Z}_p\mathbb {Z}_{p^2}$$\end{document}-linear codes, we give detailed construction of the corresponding codes. Similarly, for the values of the dimension of the kernel, we also give a construction method. Finally, pairs of rank and the dimension of the kernel of ZpZp2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {Z}_p\mathbb {Z}_{p^2}$$\end{document}-additive codes are also considered. More... »
PAGES1-14
http://scigraph.springernature.com/pub.10.1007/s10623-021-00947-8
DOIhttp://dx.doi.org/10.1007/s10623-021-00947-8
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