Information on Result #1009533

Linear OOA(2251, 2796549, F2, 3, 19) (dual of [(2796549, 3), 8389396, 20]-NRT-code), using (u, u+v)-construction based on
  1. linear OOA(243, 348, F2, 3, 9) (dual of [(348, 3), 1001, 10]-NRT-code), using
    • OOA 3-folding [i] based on linear OA(243, 1044, F2, 9) (dual of [1044, 1001, 10]-code), using
      • discarding factors / shortening the dual code based on linear OA(243, 1045, F2, 9) (dual of [1045, 1002, 10]-code), using
        • construction XX applied to C1 = C([1021,4]), C2 = C([0,6]), C3 = C1 + C2 = C([0,4]), and C∩ = C1 ∩ C2 = C([1021,6]) [i] based on
          1. linear OA(231, 1023, F2, 7) (dual of [1023, 992, 8]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−2,−1,…,4}, and designed minimum distance d ≥ |I|+1 = 8 [i]
          2. linear OA(231, 1023, F2, 7) (dual of [1023, 992, 8]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [0,6], and designed minimum distance d ≥ |I|+1 = 8 [i]
          3. linear OA(241, 1023, F2, 9) (dual of [1023, 982, 10]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−2,−1,…,6}, and designed minimum distance d ≥ |I|+1 = 10 [i]
          4. linear OA(221, 1023, F2, 5) (dual of [1023, 1002, 6]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [0,4], and designed minimum distance d ≥ |I|+1 = 6 [i]
          5. linear OA(21, 11, F2, 1) (dual of [11, 10, 2]-code), using
          6. linear OA(21, 11, F2, 1) (dual of [11, 10, 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(2251, 932182, F2, 21, 19) (dual of [(932182, 21), 19575571, 20]-NRT-code) [i]OOA Folding and Stacking with Additional Row