Information on Result #699808

Linear OA(12878, 2097187, F128, 24) (dual of [2097187, 2097109, 25]-code), using construction X applied to Ce(23) ⊂ Ce(14) based on
  1. linear OA(12870, 2097152, F128, 24) (dual of [2097152, 2097082, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
  2. linear OA(12843, 2097152, F128, 15) (dual of [2097152, 2097109, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [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
1OA(32110, 2097187, S32, 24) [i]Discarding Parts of the Base for OAs
2OA(6491, 2097187, S64, 24) [i]
3Linear OOA(12878, 1691537, F128, 2, 24) (dual of [(1691537, 2), 3382996, 25]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
4Linear OOA(12878, 1691537, F128, 3, 24) (dual of [(1691537, 3), 5074533, 25]-NRT-code) [i]
5Linear OOA(12878, 1691537, F128, 4, 24) (dual of [(1691537, 4), 6766070, 25]-NRT-code) [i]
6Digital (54, 78, 1691537)-net over F128 [i]
7Linear OOA(12878, 1048593, F128, 2, 24) (dual of [(1048593, 2), 2097108, 25]-NRT-code) [i]OOA Folding
8Linear OOA(12878, 699062, F128, 3, 24) (dual of [(699062, 3), 2097108, 25]-NRT-code) [i]
9Linear OOA(12878, 524296, F128, 4, 24) (dual of [(524296, 4), 2097106, 25]-NRT-code) [i]