Information on Result #1009501

Linear OOA(2257, 2797571, F2, 3, 18) (dual of [(2797571, 3), 8392456, 19]-NRT-code), using (u, u+v)-construction based on
  1. linear OOA(250, 1370, F2, 3, 9) (dual of [(1370, 3), 4060, 10]-NRT-code), using
    • OOA 3-folding [i] based on linear OA(250, 4110, F2, 9) (dual of [4110, 4060, 10]-code), using
      • construction X4 applied to Ce(8) ⊂ Ce(6) [i] based on
        1. linear OA(249, 4096, F2, 9) (dual of [4096, 4047, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
        2. linear OA(237, 4096, F2, 7) (dual of [4096, 4059, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
        3. linear OA(213, 14, F2, 13) (dual of [14, 1, 14]-code or 14-arc in PG(12,2)), using
        4. linear OA(21, 14, F2, 1) (dual of [14, 13, 2]-code), using
  2. linear OOA(2207, 2796201, F2, 3, 18) (dual of [(2796201, 3), 8388396, 19]-NRT-code), using
    • OOA 3-folding [i] based on linear OA(2207, large, F2, 18) (dual of [large, large−207, 19]-code), using
      • the primitive narrow-sense BCH-code C(I) with length 8388607 = 223−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [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(2259, 2797571, F2, 3, 18) (dual of [(2797571, 3), 8392454, 19]-NRT-code) [i]OOA Duplication
2Linear OOA(2257, 932523, F2, 21, 18) (dual of [(932523, 21), 19582726, 19]-NRT-code) [i]OOA Folding and Stacking with Additional Row