Information on Result #699993

Linear OA(12813, 16392, F128, 6) (dual of [16392, 16379, 7]-code), using construction X applied to Ce(5) ⊂ Ce(2) based on
  1. linear OA(12811, 16384, F128, 6) (dual of [16384, 16373, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
  2. linear OA(1285, 16384, F128, 3) (dual of [16384, 16379, 4]-code or 16384-cap in PG(4,128)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [i]
  3. linear OA(1282, 8, F128, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,128)), 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(12813, 16392, F128, 2, 6) (dual of [(16392, 2), 32771, 7]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(12813, 16392, F128, 3, 6) (dual of [(16392, 3), 49163, 7]-NRT-code) [i]
3Linear OOA(12813, 16392, F128, 4, 6) (dual of [(16392, 4), 65555, 7]-NRT-code) [i]
4Digital (7, 13, 16392)-net over F128 [i]
5Linear OOA(12813, 8196, F128, 2, 6) (dual of [(8196, 2), 16379, 7]-NRT-code) [i]OOA Folding
6Linear OOA(12813, 5464, F128, 3, 6) (dual of [(5464, 3), 16379, 7]-NRT-code) [i]
7Linear OOA(12813, 5464, F128, 4, 6) (dual of [(5464, 4), 21843, 7]-NRT-code) [i]OA Folding and Stacking
8Linear OOA(12813, 5464, F128, 6, 6) (dual of [(5464, 6), 32771, 7]-NRT-code) [i]