Information on Result #1010776

Linear OOA(3204, 3327647, F3, 3, 15) (dual of [(3327647, 3), 9982737, 16]-NRT-code), using (u, u+v)-construction based on
  1. linear OOA(354, 531446, F3, 3, 7) (dual of [(531446, 3), 1594284, 8]-NRT-code), using
    • OOA 3-folding [i] based on linear OA(354, 1594338, F3, 7) (dual of [1594338, 1594284, 8]-code), using
      • construction X4 applied to Ce(6) ⊂ Ce(4) [i] based on
        1. linear OA(353, 1594323, F3, 7) (dual of [1594323, 1594270, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
        2. linear OA(340, 1594323, F3, 5) (dual of [1594323, 1594283, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
        3. linear OA(314, 15, F3, 14) (dual of [15, 1, 15]-code or 15-arc in PG(13,3)), using
        4. 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(3205, 3327647, F3, 3, 15) (dual of [(3327647, 3), 9982736, 16]-NRT-code) [i]OOA Duplication
2Linear OOA(3206, 3327647, F3, 3, 15) (dual of [(3327647, 3), 9982735, 16]-NRT-code) [i]