Information on Result #895158

Linear OOA(3179, 4194428, F3, 2, 16) (dual of [(4194428, 2), 8388677, 17]-NRT-code), using (u, u+v)-construction based on
  1. linear OOA(328, 127, F3, 2, 8) (dual of [(127, 2), 226, 9]-NRT-code), using
    • OOA 2-folding [i] based on linear OA(328, 254, F3, 8) (dual of [254, 226, 9]-code), using
      • discarding factors / shortening the dual code based on linear OA(328, 255, F3, 8) (dual of [255, 227, 9]-code), using
        • construction XX applied to C1 = C([241,4]), C2 = C([1,6]), C3 = C1 + C2 = C([1,4]), and C∩ = C1 ∩ C2 = C([241,6]) [i] based on
          1. linear OA(321, 242, F3, 6) (dual of [242, 221, 7]-code), using the primitive BCH-code C(I) with length 242 = 35−1, defining interval I = {−1,0,…,4}, and designed minimum distance d ≥ |I|+1 = 7 [i]
          2. linear OA(320, 242, F3, 6) (dual of [242, 222, 7]-code), using the primitive narrow-sense BCH-code C(I) with length 242 = 35−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
          3. linear OA(326, 242, F3, 8) (dual of [242, 216, 9]-code), using the primitive BCH-code C(I) with length 242 = 35−1, defining interval I = {−1,0,…,6}, and designed minimum distance d ≥ |I|+1 = 9 [i]
          4. linear OA(315, 242, F3, 4) (dual of [242, 227, 5]-code), using the primitive narrow-sense BCH-code C(I) with length 242 = 35−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
          5. linear OA(31, 7, F3, 1) (dual of [7, 6, 2]-code), using
          6. linear OA(31, 6, F3, 1) (dual of [6, 5, 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(3179, 2097214, F3, 4, 16) (dual of [(2097214, 4), 8388677, 17]-NRT-code) [i]OOA Folding