Information on Result #895129

Linear OOA(3177, 4194672, F3, 2, 15) (dual of [(4194672, 2), 8389167, 16]-NRT-code), using (u, u+v)-construction based on
  1. linear OOA(327, 371, F3, 2, 7) (dual of [(371, 2), 715, 8]-NRT-code), using
    • OOA 2-folding [i] based on linear OA(327, 742, F3, 7) (dual of [742, 715, 8]-code), using
      • construction XX applied to C1 = C([363,367]), C2 = C([361,365]), C3 = C1 + C2 = C([363,365]), and C∩ = C1 ∩ C2 = C([361,367]) [i] based on
        1. linear OA(319, 728, F3, 5) (dual of [728, 709, 6]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {363,364,365,366,367}, and designed minimum distance d ≥ |I|+1 = 6 [i]
        2. linear OA(319, 728, F3, 5) (dual of [728, 709, 6]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {361,362,363,364,365}, and designed minimum distance d ≥ |I|+1 = 6 [i]
        3. linear OA(325, 728, F3, 7) (dual of [728, 703, 8]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {361,362,…,367}, and designed minimum distance d ≥ |I|+1 = 8 [i]
        4. linear OA(313, 728, F3, 3) (dual of [728, 715, 4]-code or 728-cap in PG(12,3)), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {363,364,365}, and designed minimum distance d ≥ |I|+1 = 4 [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(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(3177, 2097336, F3, 4, 15) (dual of [(2097336, 4), 8389167, 16]-NRT-code) [i]OOA Folding