Information on Result #1018504

Linear OOA(8144, 3061925, F81, 3, 9) (dual of [(3061925, 3), 9185731, 10]-NRT-code), using (u, u+v)-construction based on
  1. linear OOA(8111, 265724, F81, 3, 4) (dual of [(265724, 3), 797161, 5]-NRT-code), using
    • OA 2-folding and stacking [i] based on linear OA(8111, 531448, F81, 4) (dual of [531448, 531437, 5]-code), using
      • construction X applied to Ce(3) ⊂ Ce(1) [i] based on
        1. linear OA(8110, 531441, F81, 4) (dual of [531441, 531431, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
        2. linear OA(814, 531441, F81, 2) (dual of [531441, 531437, 3]-code), using an extension Ce(1) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,1], and designed minimum distance d ≥ |I|+1 = 2 [i]
        3. linear OA(811, 7, F81, 1) (dual of [7, 6, 2]-code), using
  2. linear OOA(8133, 2796201, F81, 3, 9) (dual of [(2796201, 3), 8388570, 10]-NRT-code), using
    • OOA 3-folding [i] based on linear OA(8133, large, F81, 9) (dual of [large, large−33, 10]-code), using
      • the expurgated narrow-sense BCH-code C(I) with length 21523361 | 818−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [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(8157, 6123850, F81, 3, 9) (dual of [(6123850, 3), 18371493, 10]-NRT-code) [i](u, u+v)-Construction for OOAs