Information on Result #1010889

Linear OOA(3233, 3327647, F3, 3, 17) (dual of [(3327647, 3), 9982708, 18]-NRT-code), using (u, u+v)-construction based on
  1. linear OOA(367, 531446, F3, 3, 8) (dual of [(531446, 3), 1594271, 9]-NRT-code), using
    • OOA 3-folding [i] based on linear OA(367, 1594338, F3, 8) (dual of [1594338, 1594271, 9]-code), using
      • construction X4 applied to Ce(7) ⊂ Ce(6) [i] based on
        1. linear OA(366, 1594323, F3, 8) (dual of [1594323, 1594257, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
        2. 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]
        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(3166, 2796201, F3, 3, 17) (dual of [(2796201, 3), 8388437, 18]-NRT-code), using
    • OOA 3-folding [i] based on linear OA(3166, large, F3, 17) (dual of [large, large−166, 18]-code), using
      • the primitive expurgated narrow-sense BCH-code C(I) with length 14348906 = 315−1, defining interval I = [0,16], and designed minimum distance d ≥ |I|+1 = 18 [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(3234, 3327647, F3, 3, 17) (dual of [(3327647, 3), 9982707, 18]-NRT-code) [i]OOA Duplication
2Linear OOA(3235, 3327647, F3, 3, 17) (dual of [(3327647, 3), 9982706, 18]-NRT-code) [i]