Information on Result #699804

Linear OA(12871, 2097183, F128, 22) (dual of [2097183, 2097112, 23]-code), using construction X applied to Ce(21) ⊂ Ce(13) based on
  1. linear OA(12864, 2097152, F128, 22) (dual of [2097152, 2097088, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
  2. linear OA(12840, 2097152, F128, 14) (dual of [2097152, 2097112, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
  3. linear OA(1287, 31, F128, 7) (dual of [31, 24, 8]-code or 31-arc in PG(6,128)), 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(32100, 2097183, S32, 22) [i]Discarding Parts of the Base for OAs
2OA(6483, 2097183, S64, 22) [i]
3Linear OOA(12871, 1551439, F128, 2, 22) (dual of [(1551439, 2), 3102807, 23]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
4Linear OOA(12871, 1551439, F128, 3, 22) (dual of [(1551439, 3), 4654246, 23]-NRT-code) [i]
5Linear OOA(12871, 1551439, F128, 4, 22) (dual of [(1551439, 4), 6205685, 23]-NRT-code) [i]
6Digital (49, 71, 1551439)-net over F128 [i]
7Linear OOA(12871, 1048591, F128, 2, 22) (dual of [(1048591, 2), 2097111, 23]-NRT-code) [i]OOA Folding
8Linear OOA(12871, 699061, F128, 3, 22) (dual of [(699061, 3), 2097112, 23]-NRT-code) [i]
9Linear OOA(12871, 524295, F128, 4, 22) (dual of [(524295, 4), 2097109, 23]-NRT-code) [i]
10Linear OOA(12871, 190653, F128, 22, 22) (dual of [(190653, 22), 4194295, 23]-NRT-code) [i]OA Folding and Stacking