Information on Result #1303733

Linear OA(1699, 1048610, F16, 20) (dual of [1048610, 1048511, 21]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(1698, 1048608, F16, 20) (dual of [1048608, 1048510, 21]-code), using
    • construction X applied to Ce(19) ⊂ Ce(13) [i] based on
      1. linear OA(1691, 1048576, F16, 20) (dual of [1048576, 1048485, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
      2. linear OA(1666, 1048576, F16, 14) (dual of [1048576, 1048510, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
      3. linear OA(167, 32, F16, 5) (dual of [32, 25, 6]-code), using
  2. linear OA(1698, 1048609, F16, 19) (dual of [1048609, 1048511, 20]-code), using Gilbert–VarÅ¡amov bound and bm = 1698 > Vbs−1(k−1) = 542345 165215 524937 472441 226079 737202 750592 573008 376726 456869 834376 555471 039127 267209 469180 136050 598597 561868 593171 [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(1699, 1048610, F16, 2, 20) (dual of [(1048610, 2), 2097121, 21]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Digital (79, 99, 1048610)-net over F16 [i]
3Linear OOA(1699, 524305, F16, 2, 20) (dual of [(524305, 2), 1048511, 21]-NRT-code) [i]OOA Folding