Information on Result #699806

Linear OA(12859, 2097183, F128, 18) (dual of [2097183, 2097124, 19]-code), using construction X applied to Ce(17) ⊂ Ce(9) based on
  1. linear OA(12852, 2097152, F128, 18) (dual of [2097152, 2097100, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
  2. linear OA(12828, 2097152, F128, 10) (dual of [2097152, 2097124, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
  3. linear OA(1287, 31, F128, 7) (dual of [31, 24, 8]-code or 31-arc in PG(6,128)), 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(12859, 2097183, F128, 2, 18) (dual of [(2097183, 2), 4194307, 19]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(12859, 2097183, F128, 3, 18) (dual of [(2097183, 3), 6291490, 19]-NRT-code) [i]
3Linear OOA(12859, 2097183, F128, 4, 18) (dual of [(2097183, 4), 8388673, 19]-NRT-code) [i]
4Digital (41, 59, 2097183)-net over F128 [i]
5Linear OOA(12859, 1048591, F128, 2, 18) (dual of [(1048591, 2), 2097123, 19]-NRT-code) [i]OOA Folding
6Linear OOA(12859, 699061, F128, 3, 18) (dual of [(699061, 3), 2097124, 19]-NRT-code) [i]
7Linear OOA(12859, 524295, F128, 4, 18) (dual of [(524295, 4), 2097121, 19]-NRT-code) [i]
8Linear OOA(12859, 233020, F128, 18, 18) (dual of [(233020, 18), 4194301, 19]-NRT-code) [i]OA Folding and Stacking