Hamming graphs and special LCD codes

Codes from adjacency matrices from the Hamming graphs Hk(n,m)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H^k(n,m)$$\end{document} are examined for the property of being special LCD codes. The special property involves being able to propose a feasible decoding algorithm for the binary codes, and also to deduce the dimension of the code from the eigenvalues of an adjacency matrix, which are known for these graphs. Some positive results are obtained, in particular for the binary and ternary codes.