Information on Result #1020007

Linear OOA(25647, 2818049, F256, 3, 12) (dual of [(2818049, 3), 8454100, 13]-NRT-code), using (u, u+v)-construction based on
  1. linear OOA(25613, 21848, F256, 3, 6) (dual of [(21848, 3), 65531, 7]-NRT-code), using
    • OOA 3-folding [i] based on linear OA(25613, 65544, F256, 6) (dual of [65544, 65531, 7]-code), using
      • construction X applied to Ce(5) ⊂ Ce(2) [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(2565, 65536, F256, 3) (dual of [65536, 65531, 4]-code or 65536-cap in PG(4,256)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [i]
        3. linear OA(2562, 8, F256, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,256)), 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(25663, 5614250, F256, 3, 12) (dual of [(5614250, 3), 16842687, 13]-NRT-code) [i](u, u+v)-Construction for OOAs
2Linear OOA(25667, 5636098, F256, 3, 12) (dual of [(5636098, 3), 16908227, 13]-NRT-code) [i]