Information on Result #1009527

Linear OOA(2243, 2796292, F2, 3, 19) (dual of [(2796292, 3), 8388633, 20]-NRT-code), using (u, u+v)-construction based on
  1. linear OOA(235, 91, F2, 3, 9) (dual of [(91, 3), 238, 10]-NRT-code), using
    • OOA 3-folding [i] based on linear OA(235, 273, F2, 9) (dual of [273, 238, 10]-code), using
      • construction XX applied to C1 = C([253,4]), C2 = C([0,6]), C3 = C1 + C2 = C([0,4]), and C∩ = C1 ∩ C2 = C([253,6]) [i] based on
        1. linear OA(225, 255, F2, 7) (dual of [255, 230, 8]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−2,−1,…,4}, and designed minimum distance d ≥ |I|+1 = 8 [i]
        2. linear OA(225, 255, F2, 7) (dual of [255, 230, 8]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [0,6], and designed minimum distance d ≥ |I|+1 = 8 [i]
        3. linear OA(233, 255, F2, 9) (dual of [255, 222, 10]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−2,−1,…,6}, and designed minimum distance d ≥ |I|+1 = 10 [i]
        4. linear OA(217, 255, F2, 5) (dual of [255, 238, 6]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [0,4], and designed minimum distance d ≥ |I|+1 = 6 [i]
        5. linear OA(21, 9, F2, 1) (dual of [9, 8, 2]-code), using
        6. linear OA(21, 9, F2, 1) (dual of [9, 8, 2]-code) (see above)
  2. linear OOA(2208, 2796201, F2, 3, 19) (dual of [(2796201, 3), 8388395, 20]-NRT-code), using
    • OOA 3-folding [i] based on linear OA(2208, large, F2, 19) (dual of [large, large−208, 20]-code), using
      • the primitive expurgated narrow-sense BCH-code C(I) with length 8388607 = 223−1, defining interval I = [0,18], and designed minimum distance d ≥ |I|+1 = 20 [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(2243, 2796292, F2, 3, 18) (dual of [(2796292, 3), 8388633, 19]-NRT-code) [i]Strength Reduction for OOAs
2Linear OOA(2244, 2796292, F2, 3, 19) (dual of [(2796292, 3), 8388632, 20]-NRT-code) [i]OOA Duplication
3Linear OOA(2243, 1398146, F2, 6, 19) (dual of [(1398146, 6), 8388633, 20]-NRT-code) [i]OOA Folding
4Linear OOA(2243, 932097, F2, 21, 19) (dual of [(932097, 21), 19573794, 20]-NRT-code) [i]OOA Folding and Stacking with Additional Row