Information on Result #1020119

Linear OOA(25658, 2818049, F256, 3, 15) (dual of [(2818049, 3), 8454089, 16]-NRT-code), using (u, u+v)-construction based on
  1. linear OOA(25615, 21848, F256, 3, 7) (dual of [(21848, 3), 65529, 8]-NRT-code), using
    • OOA 3-folding [i] based on linear OA(25615, 65544, F256, 7) (dual of [65544, 65529, 8]-code), using
      • construction X applied to Ce(6) ⊂ Ce(3) [i] based on
        1. linear OA(25613, 65536, F256, 7) (dual of [65536, 65523, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [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(2562, 8, F256, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,256)), using
  2. linear OOA(25643, 2796201, F256, 3, 15) (dual of [(2796201, 3), 8388560, 16]-NRT-code), using
    • OOA 3-folding [i] based on linear OA(25643, large, F256, 15) (dual of [large, large−43, 16]-code), using
      • the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, 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
1OOA(12867, 2818049, S128, 3, 15) [i]Discarding Parts of the Base for OOAs