Information on Result #1303723

Linear OA(1694, 1048610, F16, 19) (dual of [1048610, 1048516, 20]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(1693, 1048608, F16, 19) (dual of [1048608, 1048515, 20]-code), using
    • construction X applied to Ce(18) ⊂ Ce(12) [i] based on
      1. linear OA(1686, 1048576, F16, 19) (dual of [1048576, 1048490, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
      2. linear OA(1661, 1048576, F16, 13) (dual of [1048576, 1048515, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
      3. linear OA(167, 32, F16, 5) (dual of [32, 25, 6]-code), using
  2. linear OA(1693, 1048609, F16, 18) (dual of [1048609, 1048516, 19]-code), using Gilbert–VarÅ¡amov bound and bm = 1693 > Vbs−1(k−1) = 620655 867617 456709 433571 153487 479491 211082 910012 682945 981933 597225 291685 638818 810478 820220 981593 167337 343171 [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(1694, 1048610, F16, 2, 19) (dual of [(1048610, 2), 2097126, 20]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Digital (75, 94, 1048610)-net over F16 [i]
3Linear OOA(1694, 524305, F16, 2, 19) (dual of [(524305, 2), 1048516, 20]-NRT-code) [i]OOA Folding