Information on Result #895163

Linear OOA(3184, 4194672, F3, 2, 16) (dual of [(4194672, 2), 8389160, 17]-NRT-code), using (u, u+v)-construction based on
  1. linear OOA(333, 371, F3, 2, 8) (dual of [(371, 2), 709, 9]-NRT-code), using
    • OOA 2-folding [i] based on linear OA(333, 742, F3, 8) (dual of [742, 709, 9]-code), using
      • discarding factors / shortening the dual code based on linear OA(333, 743, F3, 8) (dual of [743, 710, 9]-code), using
        • construction XX applied to C1 = C([727,4]), C2 = C([1,6]), C3 = C1 + C2 = C([1,4]), and C∩ = C1 ∩ C2 = C([727,6]) [i] based on
          1. 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 = {−1,0,…,4}, and designed minimum distance d ≥ |I|+1 = 7 [i]
          2. linear OA(324, 728, F3, 6) (dual of [728, 704, 7]-code), using the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
          3. 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 = {−1,0,…,6}, and designed minimum distance d ≥ |I|+1 = 9 [i]
          4. linear OA(318, 728, F3, 4) (dual of [728, 710, 5]-code), using the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
          5. linear OA(31, 8, F3, 1) (dual of [8, 7, 2]-code), using
          6. linear OA(31, 7, F3, 1) (dual of [7, 6, 2]-code), using
  2. linear OOA(3151, 4194301, F3, 2, 16) (dual of [(4194301, 2), 8388451, 17]-NRT-code), using

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(3184, 2097336, F3, 4, 16) (dual of [(2097336, 4), 8389160, 17]-NRT-code) [i]OOA Folding