Information on Result #699787

Linear OA(12863, 2097175, F128, 20) (dual of [2097175, 2097112, 21]-code), using construction X applied to Ce(19) ⊂ Ce(13) 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(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(1285, 23, F128, 5) (dual of [23, 18, 6]-code or 23-arc in PG(4,128)), 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(3289, 2097175, S32, 20) [i]Discarding Parts of the Base for OAs
2OA(6474, 2097175, S64, 20) [i]
3Linear OOA(12863, 1077682, F128, 2, 20) (dual of [(1077682, 2), 2155301, 21]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
4Linear OOA(12863, 1077682, F128, 3, 20) (dual of [(1077682, 3), 3232983, 21]-NRT-code) [i]
5Linear OOA(12863, 1077682, F128, 4, 20) (dual of [(1077682, 4), 4310665, 21]-NRT-code) [i]
6Digital (43, 63, 1077682)-net over F128 [i]
7Linear OOA(12863, 1048587, F128, 2, 20) (dual of [(1048587, 2), 2097111, 21]-NRT-code) [i]OOA Folding
8Linear OOA(12863, 699058, F128, 3, 20) (dual of [(699058, 3), 2097111, 21]-NRT-code) [i]
9Linear OOA(12863, 524293, F128, 4, 20) (dual of [(524293, 4), 2097109, 21]-NRT-code) [i]