Information on Result #699805

Linear OA(12865, 2097183, F128, 20) (dual of [2097183, 2097118, 21]-code), using construction X applied to Ce(19) ⊂ Ce(11) 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(12834, 2097152, F128, 12) (dual of [2097152, 2097118, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [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(3291, 2097183, S32, 20) [i]Discarding Parts of the Base for OAs
2OA(6476, 2097183, S64, 20) [i]
3Linear OOA(12865, 1847679, F128, 2, 20) (dual of [(1847679, 2), 3695293, 21]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
4Linear OOA(12865, 1847679, F128, 3, 20) (dual of [(1847679, 3), 5542972, 21]-NRT-code) [i]
5Linear OOA(12865, 1847679, F128, 4, 20) (dual of [(1847679, 4), 7390651, 21]-NRT-code) [i]
6Digital (45, 65, 1847679)-net over F128 [i]
7Linear OOA(12865, 1048591, F128, 2, 20) (dual of [(1048591, 2), 2097117, 21]-NRT-code) [i]OOA Folding
8Linear OOA(12865, 699061, F128, 3, 20) (dual of [(699061, 3), 2097118, 21]-NRT-code) [i]
9Linear OOA(12865, 524295, F128, 4, 20) (dual of [(524295, 4), 2097115, 21]-NRT-code) [i]
10Linear OOA(12865, 209718, F128, 20, 20) (dual of [(209718, 20), 4194295, 21]-NRT-code) [i]OA Folding and Stacking