Information on Result #704487

Linear OA(3115, 758, F3, 27) (dual of [758, 643, 28]-code), using construction XX applied to C1 = C([724,21]), C2 = C([0,22]), C3 = C1 + C2 = C([0,21]), and C∩ = C1 ∩ C2 = C([724,22]) based on
  1. linear OA(3103, 728, F3, 26) (dual of [728, 625, 27]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {−4,−3,…,21}, and designed minimum distance d ≥ |I|+1 = 27 [i]
  2. linear OA(391, 728, F3, 23) (dual of [728, 637, 24]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [0,22], and designed minimum distance d ≥ |I|+1 = 24 [i]
  3. linear OA(3109, 728, F3, 27) (dual of [728, 619, 28]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {−4,−3,…,22}, and designed minimum distance d ≥ |I|+1 = 28 [i]
  4. linear OA(385, 728, F3, 22) (dual of [728, 643, 23]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [0,21], and designed minimum distance d ≥ |I|+1 = 23 [i]
  5. linear OA(36, 24, F3, 3) (dual of [24, 18, 4]-code or 24-cap in PG(5,3)), using
  6. linear OA(30, 6, F3, 0) (dual of [6, 6, 1]-code), using

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

ResultThis
result
only		Method
1Linear OOA(3115, 740, F3, 2, 27) (dual of [(740, 2), 1365, 28]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(3115, 740, F3, 3, 27) (dual of [(740, 3), 2105, 28]-NRT-code) [i]
3Linear OOA(3115, 740, F3, 4, 27) (dual of [(740, 4), 2845, 28]-NRT-code) [i]
4Linear OOA(3115, 740, F3, 5, 27) (dual of [(740, 5), 3585, 28]-NRT-code) [i]
5Digital (88, 115, 740)-net over F3 [i]
6Linear OOA(3115, 379, F3, 2, 27) (dual of [(379, 2), 643, 28]-NRT-code) [i]OOA Folding