Information on Result #699759

Linear OA(12818, 2097163, F128, 6) (dual of [2097163, 2097145, 7]-code), using construction X applied to Ce(5) ⊂ Ce(2) based on
  1. linear OA(12816, 2097152, F128, 6) (dual of [2097152, 2097136, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
  2. linear OA(1287, 2097152, F128, 3) (dual of [2097152, 2097145, 4]-code or 2097152-cap in PG(6,128)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [i]
  3. linear OA(1282, 11, F128, 2) (dual of [11, 9, 3]-code or 11-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(12818, 2097163, F128, 2, 6) (dual of [(2097163, 2), 4194308, 7]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(12818, 2097163, F128, 3, 6) (dual of [(2097163, 3), 6291471, 7]-NRT-code) [i]
3Linear OOA(12818, 2097163, F128, 4, 6) (dual of [(2097163, 4), 8388634, 7]-NRT-code) [i]
4Digital (12, 18, 2097163)-net over F128 [i]
5Linear OOA(12818, 1048581, F128, 2, 6) (dual of [(1048581, 2), 2097144, 7]-NRT-code) [i]OOA Folding
6Linear OOA(12818, 699054, F128, 3, 6) (dual of [(699054, 3), 2097144, 7]-NRT-code) [i]
7Linear OOA(12818, 699054, F128, 4, 6) (dual of [(699054, 4), 2796198, 7]-NRT-code) [i]OA Folding and Stacking
8Linear OOA(12818, 699054, F128, 6, 6) (dual of [(699054, 6), 4194306, 7]-NRT-code) [i]