Information on Result #699782

Linear OA(12838, 2097171, F128, 12) (dual of [2097171, 2097133, 13]-code), using construction X applied to Ce(11) ⊂ Ce(6) 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(12819, 2097152, F128, 7) (dual of [2097152, 2097133, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
  3. linear OA(1284, 19, F128, 4) (dual of [19, 15, 5]-code or 19-arc in PG(3,128)), 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(12838, 2097171, F128, 2, 12) (dual of [(2097171, 2), 4194304, 13]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(12838, 2097171, F128, 3, 12) (dual of [(2097171, 3), 6291475, 13]-NRT-code) [i]
3Linear OOA(12838, 2097171, F128, 4, 12) (dual of [(2097171, 4), 8388646, 13]-NRT-code) [i]
4Digital (26, 38, 2097171)-net over F128 [i]
5Linear OOA(12838, 1048585, F128, 2, 12) (dual of [(1048585, 2), 2097132, 13]-NRT-code) [i]OOA Folding
6Linear OOA(12838, 699057, F128, 3, 12) (dual of [(699057, 3), 2097133, 13]-NRT-code) [i]
7Linear OOA(12838, 524292, F128, 4, 12) (dual of [(524292, 4), 2097130, 13]-NRT-code) [i]
8Linear OOA(12838, 349528, F128, 12, 12) (dual of [(349528, 12), 4194298, 13]-NRT-code) [i]OA Folding and Stacking