Binary codes from m-ary n-cubes Q(n) (m)
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Date
2021
Journal Title
Journal ISSN
Volume Title
Publisher
American Institute of Mathematical Sciences
Abstract
We examine the binary codes from adjacency matrices of the graph with vertices the nodes
of the m-ary n-cube Qmn
and with adjacency de ned by the Lee metric. For n = 2 and m odd,
we obtain the parameters of the code and its dual, and show the codes to be LCD. We also
nd s-PD-sets of size s + 1 for s < m1
2 for the dual codes, i.e. [m2; 2m 1;m]2 codes, when
n = 2 and m 5 is odd.
Description
Keywords
Mathematics, Binary codes, Permutation decoding, Lee graph
Citation
Key, J. D., & Rodrigues, B. G. (2021). Binary codes from m-ary n-cubes Q(n) (m). Advances in Mathematics of Communications, 15(3), 507-524. 10.3934/amc.2020079