Information on Result #895125

Linear OOA(3173, 4194428, F3, 2, 15) (dual of [(4194428, 2), 8388683, 16]-NRT-code), using (u, u+v)-construction based on
  1. linear OOA(323, 127, F3, 2, 7) (dual of [(127, 2), 231, 8]-NRT-code), using
    • OOA 2-folding [i] based on linear OA(323, 254, F3, 7) (dual of [254, 231, 8]-code), using
      • construction XX applied to C1 = C([120,124]), C2 = C([118,122]), C3 = C1 + C2 = C([120,122]), and C∩ = C1 ∩ C2 = C([118,124]) [i] based on
        1. linear OA(316, 242, F3, 5) (dual of [242, 226, 6]-code), using the primitive BCH-code C(I) with length 242 = 35−1, defining interval I = {120,121,122,123,124}, and designed minimum distance d ≥ |I|+1 = 6 [i]
        2. linear OA(316, 242, F3, 5) (dual of [242, 226, 6]-code), using the primitive BCH-code C(I) with length 242 = 35−1, defining interval I = {118,119,120,121,122}, and designed minimum distance d ≥ |I|+1 = 6 [i]
        3. linear OA(321, 242, F3, 7) (dual of [242, 221, 8]-code), using the primitive BCH-code C(I) with length 242 = 35−1, defining interval I = {118,119,…,124}, and designed minimum distance d ≥ |I|+1 = 8 [i]
        4. linear OA(311, 242, F3, 3) (dual of [242, 231, 4]-code or 242-cap in PG(10,3)), using the primitive BCH-code C(I) with length 242 = 35−1, defining interval I = {120,121,122}, and designed minimum distance d ≥ |I|+1 = 4 [i]
        5. linear OA(31, 6, F3, 1) (dual of [6, 5, 2]-code), using
        6. linear OA(31, 6, F3, 1) (dual of [6, 5, 2]-code) (see above)
  2. linear OOA(3150, 4194301, F3, 2, 15) (dual of [(4194301, 2), 8388452, 16]-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(3173, 2097214, F3, 4, 15) (dual of [(2097214, 4), 8388683, 16]-NRT-code) [i]OOA Folding