Information on Result #700122

Linear OA(12855, 16416, F128, 23) (dual of [16416, 16361, 24]-code), using construction X applied to Ce(22) ⊂ Ce(11) based on
  1. linear OA(12845, 16384, F128, 23) (dual of [16384, 16339, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
  2. linear OA(12823, 16384, F128, 12) (dual of [16384, 16361, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
  3. linear OA(12810, 32, F128, 10) (dual of [32, 22, 11]-code or 32-arc in PG(9,128)), using

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(12855, 16416, F128, 2, 23) (dual of [(16416, 2), 32777, 24]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(12855, 16416, F128, 3, 23) (dual of [(16416, 3), 49193, 24]-NRT-code) [i]
3Linear OOA(12855, 16416, F128, 4, 23) (dual of [(16416, 4), 65609, 24]-NRT-code) [i]
4Digital (32, 55, 16416)-net over F128 [i]
5Linear OOA(12855, 8208, F128, 2, 23) (dual of [(8208, 2), 16361, 24]-NRT-code) [i]OOA Folding
6Linear OOA(12855, 5472, F128, 3, 23) (dual of [(5472, 3), 16361, 24]-NRT-code) [i]
7Linear OOA(12855, 4104, F128, 4, 23) (dual of [(4104, 4), 16361, 24]-NRT-code) [i]