Information on Result #1010971

Linear OOA(3235, 2796448, F3, 3, 20) (dual of [(2796448, 3), 8389109, 21]-NRT-code), using (u, u+v)-construction based on
  1. linear OOA(339, 247, F3, 3, 10) (dual of [(247, 3), 702, 11]-NRT-code), using
    • OOA 3-folding [i] based on linear OA(339, 741, F3, 10) (dual of [741, 702, 11]-code), using
      • discarding factors / shortening the dual code based on linear OA(339, 742, F3, 10) (dual of [742, 703, 11]-code), using
        • construction XX applied to C1 = C([360,367]), C2 = C([358,365]), C3 = C1 + C2 = C([360,365]), and C∩ = C1 ∩ C2 = C([358,367]) [i] based on
          1. linear OA(331, 728, F3, 8) (dual of [728, 697, 9]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {360,361,…,367}, and designed minimum distance d ≥ |I|+1 = 9 [i]
          2. linear OA(331, 728, F3, 8) (dual of [728, 697, 9]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {358,359,…,365}, and designed minimum distance d ≥ |I|+1 = 9 [i]
          3. linear OA(337, 728, F3, 10) (dual of [728, 691, 11]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {358,359,…,367}, and designed minimum distance d ≥ |I|+1 = 11 [i]
          4. linear OA(325, 728, F3, 6) (dual of [728, 703, 7]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {360,361,…,365}, and designed minimum distance d ≥ |I|+1 = 7 [i]
          5. linear OA(31, 7, F3, 1) (dual of [7, 6, 2]-code), using
          6. linear OA(31, 7, F3, 1) (dual of [7, 6, 2]-code) (see above)
  2. linear OOA(3196, 2796201, F3, 3, 20) (dual of [(2796201, 3), 8388407, 21]-NRT-code), using
    • OOA 3-folding [i] based on linear OA(3196, large, F3, 20) (dual of [large, large−196, 21]-code), using
      • the primitive expurgated narrow-sense BCH-code C(I) with length 14348906 = 315−1, defining interval I = [0,19], and designed minimum distance d ≥ |I|+1 = 21 [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.