Information on Result #691716

Linear OA(1694, 1048627, F16, 18) (dual of [1048627, 1048533, 19]-code), using construction X applied to Ce(17) ⊂ Ce(8) based on
  1. linear OA(1681, 1048576, F16, 18) (dual of [1048576, 1048495, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
  2. linear OA(1641, 1048576, F16, 9) (dual of [1048576, 1048535, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
  3. linear OA(1613, 51, F16, 8) (dual of [51, 38, 9]-code), using
    • the BCH-code C(I) with length 51 | 162−1, defining interval I = {1,5,9,…,29}, and designed minimum distance d ≥ |I|+1 = 9 [i]

Mode: Constructive and 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, 116514, F16, 18, 18) (dual of [(116514, 18), 2097158, 19]-NRT-code) [i]OA Folding and Stacking