Information on Result #700104

Linear OA(12872, 16413, F128, 32) (dual of [16413, 16341, 33]-code), using construction X applied to Ce(31) ⊂ Ce(21) based on
  1. linear OA(12863, 16384, F128, 32) (dual of [16384, 16321, 33]-code), using an extension Ce(31) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,31], and designed minimum distance d ≥ |I|+1 = 32 [i]
  2. linear OA(12843, 16384, F128, 22) (dual of [16384, 16341, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
  3. linear OA(1289, 29, F128, 9) (dual of [29, 20, 10]-code or 29-arc in PG(8,128)), 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
1OA(6484, 16413, S64, 32) [i]Discarding Parts of the Base for OAs
2Linear OOA(12872, 9191, F128, 2, 32) (dual of [(9191, 2), 18310, 33]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
3Linear OOA(12872, 9191, F128, 3, 32) (dual of [(9191, 3), 27501, 33]-NRT-code) [i]
4Linear OOA(12872, 9191, F128, 4, 32) (dual of [(9191, 4), 36692, 33]-NRT-code) [i]
5Digital (40, 72, 9191)-net over F128 [i]
6Linear OOA(12872, 8206, F128, 2, 32) (dual of [(8206, 2), 16340, 33]-NRT-code) [i]OOA Folding
7Linear OOA(12872, 5471, F128, 3, 32) (dual of [(5471, 3), 16341, 33]-NRT-code) [i]
8Linear OOA(12872, 4103, F128, 4, 32) (dual of [(4103, 4), 16340, 33]-NRT-code) [i]