Information on Result #1009316

Linear OOA(2212, 2861736, F2, 3, 15) (dual of [(2861736, 3), 8584996, 16]-NRT-code), using (u, u+v)-construction based on
  1. linear OOA(250, 65535, F2, 3, 7) (dual of [(65535, 3), 196555, 8]-NRT-code), using
  2. linear OOA(2162, 2796201, F2, 3, 15) (dual of [(2796201, 3), 8388441, 16]-NRT-code), using
    • OOA 3-folding [i] based on linear OA(2162, large, F2, 15) (dual of [large, large−162, 16]-code), using
      • the primitive expurgated narrow-sense BCH-code C(I) with length 8388607 = 223−1, defining interval I = [0,14], and designed minimum distance d ≥ |I|+1 = 16 [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, k and s, k and t, m and s, m and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

ResultThis
result
only		Method
1Linear OOA(2212, 2861736, F2, 3, 14) (dual of [(2861736, 3), 8584996, 15]-NRT-code) [i]Strength Reduction for OOAs
2Linear OOA(2213, 2861736, F2, 3, 15) (dual of [(2861736, 3), 8584995, 16]-NRT-code) [i]OOA Duplication
3Linear OOA(2214, 2861736, F2, 3, 15) (dual of [(2861736, 3), 8584994, 16]-NRT-code) [i]
4Linear OOA(2212, 2573839, F2, 4, 15) (dual of [(2573839, 4), 10295144, 16]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
5Linear OOA(2212, 2573839, F2, 5, 15) (dual of [(2573839, 5), 12868983, 16]-NRT-code) [i]
6Linear OOA(2212, 2573839, F2, 6, 15) (dual of [(2573839, 6), 15442822, 16]-NRT-code) [i]
7Linear OOA(2212, 2573839, F2, 7, 15) (dual of [(2573839, 7), 18016661, 16]-NRT-code) [i]
8Linear OOA(2212, 2573839, F2, 8, 15) (dual of [(2573839, 8), 20590500, 16]-NRT-code) [i]
9Digital (197, 212, 2573839)-net over F2 [i]
10Linear OOA(2212, 1430868, F2, 6, 15) (dual of [(1430868, 6), 8584996, 16]-NRT-code) [i]OOA Folding