Information on Result #1303753

Linear OA(16104, 1048610, F16, 21) (dual of [1048610, 1048506, 22]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(16103, 1048608, F16, 21) (dual of [1048608, 1048505, 22]-code), using
    • construction X applied to Ce(20) ⊂ Ce(14) [i] based on
      1. linear OA(1696, 1048576, F16, 21) (dual of [1048576, 1048480, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
      2. linear OA(1671, 1048576, F16, 15) (dual of [1048576, 1048505, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
      3. linear OA(167, 32, F16, 5) (dual of [32, 25, 6]-code), using
  2. linear OA(16103, 1048609, F16, 20) (dual of [1048609, 1048506, 21]-code), using Gilbert–VarÅ¡amov bound and bm = 16103 > Vbs−1(k−1) = 448971 910223 963428 047539 735841 154341 313090 258830 540225 268462 361422 330366 219926 157901 604689 163468 908230 576014 554056 093171 [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(16104, 1048610, F16, 2, 21) (dual of [(1048610, 2), 2097116, 22]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Digital (83, 104, 1048610)-net over F16 [i]
3Linear OOA(16104, 524305, F16, 2, 21) (dual of [(524305, 2), 1048506, 22]-NRT-code) [i]OOA Folding