Information on Result #1303771

Linear OA(16108, 1048609, F16, 22) (dual of [1048609, 1048501, 23]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(16107, 1048607, F16, 22) (dual of [1048607, 1048500, 23]-code), using
    • construction X applied to Ce(21) ⊂ Ce(16) [i] based on
      1. linear OA(16101, 1048576, F16, 22) (dual of [1048576, 1048475, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
      2. linear OA(1676, 1048576, F16, 17) (dual of [1048576, 1048500, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
      3. linear OA(166, 31, F16, 4) (dual of [31, 25, 5]-code), using
  2. linear OA(16107, 1048608, F16, 21) (dual of [1048608, 1048501, 22]-code), using Gilbert–VarÅ¡amov bound and bm = 16107 > Vbs−1(k−1) = 353083 542769 778286 159053 903292 879633 438608 513276 807321 841008 434469 923162 797377 314897 661381 438096 266443 145068 147955 837072 963831 [i]
  3. linear OA(160, 1, F16, 0) (dual of [1, 1, 1]-code), using

Mode: Linear.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

ResultThis
result
only		Method
1Linear OOA(16108, 1048609, F16, 2, 22) (dual of [(1048609, 2), 2097110, 23]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Digital (86, 108, 1048609)-net over F16 [i]