Bounds on the minimum distance of additive quantum codes

Bounds on [[104,70]]2

lower bound:7
upper bound:10

Construction

Construction of a [[104,70,7]] quantum code:
[1]:  [[256, 222, 7]] quantum code over GF(2^2)
     Extended BCH code with parameters 255 6
[2]:  [[104, 70, 7]] quantum code over GF(2^2)
     Shortening of [1] at { 2, 3, 4, 5, 6, 8, 10, 12, 14, 15, 16, 17, 18, 19, 20, 22, 25, 28, 29, 30, 31, 33, 35, 36, 37, 38, 40, 42, 43, 44, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 58, 59, 60, 61, 63, 64, 66, 68, 69, 70, 71, 72, 73, 74, 75, 77, 78, 80, 81, 82, 84, 85, 86, 87, 89, 90, 91, 92, 93, 95, 96, 97, 99, 100, 101, 102, 103, 105, 106, 107, 109, 110, 111, 115, 117, 118, 119, 121, 122, 123, 125, 127, 131, 132, 133, 137, 138, 139, 140, 142, 143, 145, 147, 148, 150, 157, 158, 159, 161, 163, 164, 167, 170, 172, 174, 175, 176, 177, 179, 185, 189, 192, 198, 200, 201, 202, 204, 205, 206, 211, 212, 213, 217, 218, 219, 220, 221, 224, 226, 228, 229, 231, 233, 237, 240, 241, 247, 248, 249, 250, 255 }

    stabilizer matrix:

      [1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 0 1 1 0 0 0 0 1 1 0 0 1 0 1 1 1 0 0 1 1 1 1 1 0 1 0 1 0 1 1 0 1 0 1 0 1 0 0 0 0 1 0 1 1 0 0 0 1 0 0 0 0 0 0 1 1 1 0 0 1 0|0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 0 0 1 1 0 1 1 0 0 0 1 1 0 0 0 1 0 0 0 0 1 1 1 1 0 1 1 1 1 0 1 1 0 1 1 0 0 0 1 1 1 0 1 1 0 0 0 0 0 1 1 0 1 0 1 1 1 1 1 1 1 1 0 1 1 1 1 1 0 1 0 0 1 0 1 0 1 1 0 1 1 0 0 0 0]
      [0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 1 1 1 1 1 1 0 0 1 0 0 1 1 0 1 0 1 1 0 1 0 1 1 1 0 1 1 1 1 0 0 1 1 0 1 0 1 0 0 0 0 1 0 1 0 0 0 1 1 0 0 1 0 1 1|0 0 0 0 0 0 0 0 0 1 1 1 0 0 1 1 1 1 1 1 0 0 1 0 1 1 0 0 1 0 0 1 1 0 0 1 0 1 0 1 0 1 1 1 1 0 1 0 1 0 1 0 0 1 0 1 1 0 0 1 0 0 1 0 1 1 0 1 1 1 1 1 0 1 0 0 0 0 0 1 1 1 1 0 1 0 0 0 1 0 1 1 0 1 0 0 1 1 1 1 0 1 0 0]
      [0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 0 0 1 0 0 1 0 1 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 1 1 0 1 1 1 1 1 1 0 0 1 0 1 1 1|0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 1 0 0 0 1 1 0 1 0 0 0 1 0 0 0 0 0 1 0 0 0 1 1 0 1 1 0 1 1 1 1 1 1 0 1 0 1 1 0 1 1 0 1 1 1 1 0 0 1 0 0 1 1 1 1 1 1 1 1 0 0 1 0 0 1 1 1 0 1 0 1 1 0 1 0 1 1 0 1 0 0 0 0 0 0 1 0 1]
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      [0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 0 1 1 0 0 1 0 1 0 0 0 1 1 0 0 1 1 0 1 0 1 0 1 1 0 1 0 0 0 0 1 0 0 1 0 1 0 1 0 1 0 1 0 0 0 1 0 0 1 1 0 1 1 1 1 0 0 1 0 0 1 0 0 0 0 1 1 1 1 0 1 1 1 1 1|0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 1 1 0 0 0 1 1 0 1 1 1 1 0 1 1 0 0 0 0 0 1 0 1 0 0 0 1 0 0 1 0 1 0 1 0 0 1 1 0 1 0 1 0 0 1 0 0 0 1 0 1 0 1 0 1 1 1 1 0 1 1 1 0 0 1 0 0 1 0 1 1 1 0 1 1 1 0 0 1 0 1 1 1 0 1 1 0]
      [0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 0 1 1 0 1 1 1 0 0 0 1 0 1 1 1 0 1 1 0 0 0 1 0 0 0 1 1 1 0 0 0 1 1 1 0 1 1 0 0 1 1 0 0 1 1 1 0 1 1 0 0 1 0 0 0 0 1 1 0 0 0 0 1 0 0 0 1 1 0 0 0 0|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 0 0 1 1 0 1 1 1 0 1 0 1 1 1 1 1 1 1 1 0 0 1 0 1 1 1 0 0 1 0 0 0 1 0 1 1 0 0 0 0 0 0 1 1 1 1 0 0 1 0 0 1 0 1 1 1 1 1 0 0 1 0 0 0 1 0 0 1 1 1 0 1 0 0 0 0 0 0 1 1 0]
      [0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 1 1 1 0 1 1 0 1 1 1 0 0 0 0 1 1 0 0 1 1 1 0 0 0 0 1 0 1 0 1 0 1 0 0 0 1 1 1 1 1 0 0 0 0 1 0 0 0 0 1 0 1 0 1 1 1 0 1 0 1 1 0 1 0 1 1 0 0 1 1 0 1 0 0|0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 1 1 1 0 1 1 0 1 0 0 1 0 0 0 1 1 0 1 0 0 0 1 0 1 1 0 1 1 1 1 0 1 0 1 1 1 0 0 1 1 1 0 1 1 0 1 1 0 0 0 1 0 1 0 1 1 1 0 1 1 0 1 0 0 0 1 0 1 1 1 0 1 0 0 0 1 0 0 0 0 0 0 1 1 1 0 1 1 0]
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      [0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 1 1 0 0 1 1 1 1 0 1 1 0 0 1 0 1 0 0 0 0 1 1 0 0 0 1 1 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0 0 1 0 1 1 0 1 1 0 1 1 1 1 1 1 0 1 1 1 1 0 0 0 1 1 0 0 0 0|0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 1 0 1 0 1 0 1 1 0 1 1 0 1 1 0 0 0 1 0 0 0 0 1 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 1 0 0 1 0 1 1 0 1 0 1 1 0 1 1 1 1 1 1 0 1 0 1 0 0 1 0 0 0 1 0 1 0 0 1 1 1 0 1 1 0 0 1 0 0 1 1 1 0]
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      [0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 0 0 1 1 0 1 0 1 1 1 1 0 0 0 1 0 1 1 0 0 0 0 0 1 1 1 0 0 0 1 1 0 1 0 1 0 0 0 1 0 1 0 1 0 1 0 1 1 0 0 1 0 0 1 0 1 0 1 0 0 0 1 1 1 1 1 1 0 1 1 0 0 0 1|0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 1 0 1 0 1 1 1 1 1 0 0 0 0 0 1 0 1 0 0 1 0 0 0 0 0 0 1 1 0 1 1 1 1 0 1 0 0 1 0 0 0 1 0 1 0 1 0 0 1 0 1 0 1 1 1 1 1 1 0 0 1 1 0 1 0 0 1 1 1 0 1 1 0 0 1 1 1 0 0 1 1 0 1 0 0 0 0 1]
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last modified: 2009-01-27

Notes


This page is maintained by Markus Grassl (codes@codetables.de). Last change: 23.10.2014