Information on Result #1010778

Linear OOA(3208, 4390529, F3, 3, 15) (dual of [(4390529, 3), 13171379, 16]-NRT-code), using (u, u+v)-construction based on
  1. linear OOA(358, 1594328, F3, 3, 7) (dual of [(1594328, 3), 4782926, 8]-NRT-code), using
    • OOA 3-folding [i] based on linear OA(358, 4782984, F3, 7) (dual of [4782984, 4782926, 8]-code), using
      • construction X applied to Ce(6) ⊂ Ce(4) [i] based on
        1. linear OA(357, 4782969, F3, 7) (dual of [4782969, 4782912, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
        2. linear OA(343, 4782969, F3, 5) (dual of [4782969, 4782926, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
        3. linear OA(31, 15, F3, 1) (dual of [15, 14, 2]-code), using
  2. linear OOA(3150, 2796201, F3, 3, 15) (dual of [(2796201, 3), 8388453, 16]-NRT-code), using
    • OOA 3-folding [i] based on linear OA(3150, large, F3, 15) (dual of [large, large−150, 16]-code), using
      • the primitive narrow-sense BCH-code C(I) with length 14348906 = 315−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [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

The following results depend on this result:

ResultThis
result
only		Method
1Linear OOA(3209, 4390529, F3, 3, 15) (dual of [(4390529, 3), 13171378, 16]-NRT-code) [i]OOA Duplication