Information on Result #1303745

Linear OA(16102, 1048604, F16, 21) (dual of [1048604, 1048502, 22]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(16100, 1048600, F16, 21) (dual of [1048600, 1048500, 22]-code), using
    • construction X applied to Ce(20) ⊂ Ce(16) [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(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(164, 24, F16, 3) (dual of [24, 20, 4]-code or 24-cap in PG(3,16)), using
  2. linear OA(16100, 1048602, F16, 20) (dual of [1048602, 1048502, 21]-code), using Gilbert–VarÅ¡amov bound and bm = 16100 > Vbs−1(k−1) = 448914 967891 557595 473389 475834 598982 992684 900212 753435 743761 060143 626871 987946 968598 149711 009552 035934 859474 550012 859016 [i]
  3. linear OA(160, 2, F16, 0) (dual of [2, 2, 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(16102, 1048604, F16, 2, 21) (dual of [(1048604, 2), 2097106, 22]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Digital (81, 102, 1048604)-net over F16 [i]
3Linear OOA(16102, 524302, F16, 2, 21) (dual of [(524302, 2), 1048502, 22]-NRT-code) [i]OOA Folding