Information on Result #1020146

Linear OOA(25663, 2818049, F256, 3, 16) (dual of [(2818049, 3), 8454084, 17]-NRT-code), using (u, u+v)-construction based on
  1. linear OOA(25617, 21848, F256, 3, 8) (dual of [(21848, 3), 65527, 9]-NRT-code), using
    • OOA 3-folding [i] based on linear OA(25617, 65544, F256, 8) (dual of [65544, 65527, 9]-code), using
      • construction X applied to Ce(7) ⊂ Ce(4) [i] based on
        1. linear OA(25615, 65536, F256, 8) (dual of [65536, 65521, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
        2. linear OA(2569, 65536, F256, 5) (dual of [65536, 65527, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [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(25646, 2796201, F256, 3, 16) (dual of [(2796201, 3), 8388557, 17]-NRT-code), using
    • OOA 3-folding [i] based on linear OA(25646, large, F256, 16) (dual of [large, large−46, 17]-code), using
      • the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,15], and designed minimum distance d ≥ |I|+1 = 17 [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(12872, 2818049, S128, 3, 16) [i]Discarding Parts of the Base for OOAs