Information on Result #1020006

Linear OOA(25646, 2818048, F256, 3, 12) (dual of [(2818048, 3), 8454098, 13]-NRT-code), using (u, u+v)-construction based on
  1. linear OOA(25612, 21847, F256, 3, 6) (dual of [(21847, 3), 65529, 7]-NRT-code), using
    • OOA 3-folding [i] based on linear OA(25612, 65541, F256, 6) (dual of [65541, 65529, 7]-code), using
      • construction X applied to Ce(5) ⊂ Ce(3) [i] based on
        1. linear OA(25611, 65536, F256, 6) (dual of [65536, 65525, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
        2. linear OA(2567, 65536, F256, 4) (dual of [65536, 65529, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
        3. linear OA(2561, 5, F256, 1) (dual of [5, 4, 2]-code), using
  2. linear OOA(25634, 2796201, F256, 3, 12) (dual of [(2796201, 3), 8388569, 13]-NRT-code), using
    • OOA 3-folding [i] based on linear OA(25634, large, F256, 12) (dual of [large, large−34, 13]-code), using
      • the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, 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(25662, 5614249, F256, 3, 12) (dual of [(5614249, 3), 16842685, 13]-NRT-code) [i](u, u+v)-Construction for OOAs
2Linear OOA(25666, 5636096, F256, 3, 12) (dual of [(5636096, 3), 16908222, 13]-NRT-code) [i]
3Linear OOA(25646, 1409024, F256, 6, 12) (dual of [(1409024, 6), 8454098, 13]-NRT-code) [i]OOA Folding