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I used v2.17-r941 of minimap2. The defaults shown by the --help are k=15, w=10.

Usage: minimap2 [options] <target.fa>|<target.idx> [query.fa] [...]
Options:
  Indexing:
    -H           use homopolymer-compressed k-mer (preferrable for PacBio)
    -k INT       k-mer size (no larger than 28) [15]
    -w INT       minimizer window size [10]

From the 2014 reference for Kraken: "By default, Kraken builds the database with k = 31...By default Kraken uses 15-bp minimizers [this is the window length]"

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