Information on Result #1009404

Linear OOA(2258, 2883589, F2, 3, 16) (dual of [(2883589, 3), 8650509, 17]-NRT-code), using (u, u+v)-construction based on
  1. linear OOA(274, 87388, F2, 3, 8) (dual of [(87388, 3), 262090, 9]-NRT-code), using
    • OOA 3-folding [i] based on linear OA(274, 262164, F2, 8) (dual of [262164, 262090, 9]-code), using
      • strength reduction [i] based on linear OA(274, 262164, F2, 9) (dual of [262164, 262090, 10]-code), using
        • construction X4 applied to Ce(8) ⊂ Ce(6) [i] based on
          1. linear OA(273, 262144, F2, 9) (dual of [262144, 262071, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 262143 = 218−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
          2. linear OA(255, 262144, F2, 7) (dual of [262144, 262089, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 262143 = 218−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
          3. linear OA(219, 20, F2, 19) (dual of [20, 1, 20]-code or 20-arc in PG(18,2)), using
          4. linear OA(21, 20, F2, 1) (dual of [20, 19, 2]-code), using
  2. linear OOA(2184, 2796201, F2, 3, 16) (dual of [(2796201, 3), 8388419, 17]-NRT-code), using
    • OOA 3-folding [i] based on linear OA(2184, large, F2, 16) (dual of [large, large−184, 17]-code), using
      • the primitive narrow-sense BCH-code C(I) with length 8388607 = 223−1, defining interval I = [1,16], 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

None.