Information on Result #699818

Linear OA(12874, 2097195, F128, 22) (dual of [2097195, 2097121, 23]-code), using construction X applied to Ce(21) ⊂ Ce(10) 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(12831, 2097152, F128, 11) (dual of [2097152, 2097121, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
  3. linear OA(12810, 43, F128, 10) (dual of [43, 33, 11]-code or 43-arc in PG(9,128)), 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
1Linear OOA(12874, 2097195, F128, 2, 22) (dual of [(2097195, 2), 4194316, 23]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(12874, 2097195, F128, 3, 22) (dual of [(2097195, 3), 6291511, 23]-NRT-code) [i]
3Linear OOA(12874, 2097195, F128, 4, 22) (dual of [(2097195, 4), 8388706, 23]-NRT-code) [i]
4Digital (52, 74, 2097195)-net over F128 [i]
5Linear OOA(12874, 1048597, F128, 2, 22) (dual of [(1048597, 2), 2097120, 23]-NRT-code) [i]OOA Folding
6Linear OOA(12874, 699065, F128, 3, 22) (dual of [(699065, 3), 2097121, 23]-NRT-code) [i]
7Linear OOA(12874, 524298, F128, 4, 22) (dual of [(524298, 4), 2097118, 23]-NRT-code) [i]
8Linear OOA(12874, 190654, F128, 22, 22) (dual of [(190654, 22), 4194314, 23]-NRT-code) [i]OA Folding and Stacking