Information on Result #699812

Linear OA(12866, 2097187, F128, 20) (dual of [2097187, 2097121, 21]-code), using construction X applied to Ce(19) ⊂ Ce(10) based on
  1. linear OA(12858, 2097152, F128, 20) (dual of [2097152, 2097094, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
  2. linear OA(12831, 2097152, F128, 11) (dual of [2097152, 2097121, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
  3. linear OA(1288, 35, F128, 8) (dual of [35, 27, 9]-code or 35-arc in PG(7,128)), 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(12866, 2097187, F128, 2, 20) (dual of [(2097187, 2), 4194308, 21]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(12866, 2097187, F128, 3, 20) (dual of [(2097187, 3), 6291495, 21]-NRT-code) [i]
3Linear OOA(12866, 2097187, F128, 4, 20) (dual of [(2097187, 4), 8388682, 21]-NRT-code) [i]
4Digital (46, 66, 2097187)-net over F128 [i]
5Linear OOA(12866, 1048593, F128, 2, 20) (dual of [(1048593, 2), 2097120, 21]-NRT-code) [i]OOA Folding
6Linear OOA(12866, 699062, F128, 3, 20) (dual of [(699062, 3), 2097120, 21]-NRT-code) [i]
7Linear OOA(12866, 524296, F128, 4, 20) (dual of [(524296, 4), 2097118, 21]-NRT-code) [i]