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Table 2 Summary of our methods for lengths 5, 21, and 10 to refer to 1- and 2-mismatch and 1- and 2-gap sequences

From: Perfect Hamming code with a hash table for faster genome mapping

length condition #keys #words ratio f(s, K) when s = c(s) f(s, K) when c ≠ c(s)
5 1-mismatch 6.625 16 41.4% 1 + 15x 1 + 15x + 42x2 + 54x3
  2-mismatches 27.25 106 25.7% 1 + 15 + 90x2 + 210x3 + 180x4 1 + 15 + 90x2 + 170x3 + 156x4
  1-gap 3.25 4 81.3% 4 + 12x 4 + 60x
  2-gaps 10 16 62.5% 16 + 36x + 108x2 1
21 1-mismatch 30.53 64 47.7% 1 + 63x 1 + 63x + 210x2 + 1710x3
  2-mismatches 611.31 1954 31.3% 1 + 63x + 1890x2 + 4410x3 + 34020x4 1 + 63x + 1890x2 + 5650x3 + 31500x4
  1-gap 3.81 4 95.3% 4 + 60x 4 + 252x
  2-gaps 13.87 16 86.7% 16 + 84x + 540x2 16 + 48x + 960x2
10: Serialize 1-mismatch 12.25 31 39.5% 1 + 30x + 225x2 1 + 30x + 170x2 + 538x3 + 1089x4 + 1620x5 2
10: Parallelize 1-mismatch 13.25 31 44.1% 1 + 30x 1 + 30x + 84x2 + 108x3 3
  1. 1 :s always includes one code word. 2: neither the first half nor the second half are code words. The reference formula when one of the two halves is a code word is 1 + 30x2 + 267x2 + 684x3 + 810x4. 3: neither the first half or second half are code words. The reference formula when one of the two halves is a code word is 1 + 30x2 + 42x2 + 54x3.