Information on Result #1303707

Linear OA(1684, 1048610, F16, 17) (dual of [1048610, 1048526, 18]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(1683, 1048608, F16, 17) (dual of [1048608, 1048525, 18]-code), using
    • construction X applied to Ce(16) ⊂ Ce(10) [i] based on
      1. 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]
      2. linear OA(1651, 1048576, F16, 11) (dual of [1048576, 1048525, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
      3. linear OA(167, 32, F16, 5) (dual of [32, 25, 6]-code), using
  2. linear OA(1683, 1048609, F16, 16) (dual of [1048609, 1048526, 17]-code), using Gilbert–VarÅ¡amov bound and bm = 1683 > Vbs−1(k−1) = 682375 934352 272467 710614 302455 931600 613801 454964 372929 533539 633528 191006 338985 131069 790872 499421 [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(1684, 1048610, F16, 2, 17) (dual of [(1048610, 2), 2097136, 18]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Digital (67, 84, 1048610)-net over F16 [i]