Information on Result #699794

Linear OA(12870, 2097179, F128, 22) (dual of [2097179, 2097109, 23]-code), using construction X applied to Ce(21) ⊂ Ce(14) 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(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(1286, 27, F128, 6) (dual of [27, 21, 7]-code or 27-arc in PG(5,128)), 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(3298, 2097179, S32, 22) [i]Discarding Parts of the Base for OAs
2OA(6482, 2097179, S64, 22) [i]
3Linear OOA(12870, 1217233, F128, 2, 22) (dual of [(1217233, 2), 2434396, 23]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
4Linear OOA(12870, 1217233, F128, 3, 22) (dual of [(1217233, 3), 3651629, 23]-NRT-code) [i]
5Linear OOA(12870, 1217233, F128, 4, 22) (dual of [(1217233, 4), 4868862, 23]-NRT-code) [i]
6Digital (48, 70, 1217233)-net over F128 [i]
7Linear OOA(12870, 1048589, F128, 2, 22) (dual of [(1048589, 2), 2097108, 23]-NRT-code) [i]OOA Folding
8Linear OOA(12870, 699059, F128, 3, 22) (dual of [(699059, 3), 2097107, 23]-NRT-code) [i]
9Linear OOA(12870, 524294, F128, 4, 22) (dual of [(524294, 4), 2097106, 23]-NRT-code) [i]