Information on Result #699758

Linear OA(12821, 2097163, F128, 7) (dual of [2097163, 2097142, 8]-code), using construction X applied to Ce(6) ⊂ Ce(3) based on
  1. linear OA(12819, 2097152, F128, 7) (dual of [2097152, 2097133, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
  2. linear OA(12810, 2097152, F128, 4) (dual of [2097152, 2097142, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [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(12821, 2097163, F128, 2, 7) (dual of [(2097163, 2), 4194305, 8]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(12821, 2097163, F128, 3, 7) (dual of [(2097163, 3), 6291468, 8]-NRT-code) [i]
3Linear OOA(12821, 2097163, F128, 4, 7) (dual of [(2097163, 4), 8388631, 8]-NRT-code) [i]
4Digital (14, 21, 2097163)-net over F128 [i]
5Linear OOA(12821, 1048581, F128, 2, 7) (dual of [(1048581, 2), 2097141, 8]-NRT-code) [i]OOA Folding
6Linear OOA(12821, 699054, F128, 3, 7) (dual of [(699054, 3), 2097141, 8]-NRT-code) [i]
7Linear OOA(12821, 699054, F128, 4, 7) (dual of [(699054, 4), 2796195, 8]-NRT-code) [i]OOA Folding and Stacking with Additional Row
8Linear OOA(12821, 699054, F128, 7, 7) (dual of [(699054, 7), 4893357, 8]-NRT-code) [i]