@inproceedings{a87db236c7e24af384ebd25f85cd3898,

title = "Connections between the Error Probability and the r-wise Hamming Distances",

abstract = "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.",

author = "Lin, {Hsuan Yin} and Moser, {Stefan M.} and Po-Ning Chen",

year = "2019",

month = mar,

day = "8",

doi = "10.23919/ISITA.2018.8664296",

language = "English",

series = "Proceedings of 2018 International Symposium on Information Theory and Its Applications, ISITA 2018",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

pages = "130--134",

booktitle = "Proceedings of 2018 International Symposium on Information Theory and Its Applications, ISITA 2018",

address = "United States",

note = "null ; Conference date: 28-10-2018 Through 31-10-2018",

}