Information on Result #699766

Linear OA(12837, 2097167, F128, 12) (dual of [2097167, 2097130, 13]-code), using construction X applied to Ce(11) ⊂ Ce(7) based on
  1. 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]
  2. linear OA(12822, 2097152, F128, 8) (dual of [2097152, 2097130, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
  3. linear OA(1283, 15, F128, 3) (dual of [15, 12, 4]-code or 15-arc in PG(2,128) or 15-cap in PG(2,128)), 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(1665, 2097167, S16, 12) [i]Discarding Parts of the Base for OAs
2OA(3252, 2097167, S32, 12) [i]
3OA(6444, 2097167, S64, 12) [i]
4Linear OOA(12837, 1374444, F128, 2, 12) (dual of [(1374444, 2), 2748851, 13]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
5Linear OOA(12837, 1374444, F128, 3, 12) (dual of [(1374444, 3), 4123295, 13]-NRT-code) [i]
6Linear OOA(12837, 1374444, F128, 4, 12) (dual of [(1374444, 4), 5497739, 13]-NRT-code) [i]
7Digital (25, 37, 1374444)-net over F128 [i]
8Linear OOA(12837, 1048583, F128, 2, 12) (dual of [(1048583, 2), 2097129, 13]-NRT-code) [i]OOA Folding
9Linear OOA(12837, 699055, F128, 3, 12) (dual of [(699055, 3), 2097128, 13]-NRT-code) [i]
10Linear OOA(12837, 524291, F128, 4, 12) (dual of [(524291, 4), 2097127, 13]-NRT-code) [i]