Information on Result #1019236

Linear OOA(12857, 2801664, F128, 3, 12) (dual of [(2801664, 3), 8404935, 13]-NRT-code), using (u, u+v)-construction based on
  1. linear OOA(12812, 5463, F128, 3, 6) (dual of [(5463, 3), 16377, 7]-NRT-code), using
    • OOA 3-folding [i] based on linear OA(12812, 16389, F128, 6) (dual of [16389, 16377, 7]-code), using
      • construction X applied to Ce(5) ⊂ Ce(3) [i] based on
        1. linear OA(12811, 16384, F128, 6) (dual of [16384, 16373, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
        2. linear OA(1287, 16384, F128, 4) (dual of [16384, 16377, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
        3. linear OA(1281, 5, F128, 1) (dual of [5, 4, 2]-code), using
  2. linear OOA(12845, 2796201, F128, 3, 12) (dual of [(2796201, 3), 8388558, 13]-NRT-code), using
    • OOA 3-folding [i] based on linear OA(12845, large, F128, 12) (dual of [large, large−45, 13]-code), using
      • the expurgated narrow-sense BCH-code C(I) with length 9256395 | 1284−1, defining interval I = [0,11], and designed minimum distance d ≥ |I|+1 = 13 [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(12878, 5597865, F128, 3, 12) (dual of [(5597865, 3), 16793517, 13]-NRT-code) [i](u, u+v)-Construction for OOAs