Summary
The 2018 International Symposium on Information Theory and Its Applications　(ISITA2018)
2018
Session Number:Mo-PM-1-2
Session:
Number:Mo-PM-1-2.4
Connections Between the Error Probability and the r-wise Hamming Distances
Hsuan-Yin Lin, Stefan M. Moser, Po-Ning Chen,
pp.130-134
Publication Date:2018/10/18
Online ISSN:2188-5079
DOI:10.34385/proc.55.Mo-PM-1-2.4
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Summary:
An extension from the pairwise Hamming distance to the r-wise Hamming distance is presented. It can be used to fully characterize the maximum-likelihood decoding (MLD) error of an arbitrary code over the binary erasure channel (BEC). By noting that good codes always have large minimum r-wise Hamming distances for all r, a new design criterion for a code is introduced: the minimum r-wise Hamming distance. We then prove an upper bound for the minimum r-wise Hamming distance of an arbitrary code, called the generalized Plotkin bound, and provide a class of (nonlinear) codes that achieve the bound for every r.