Information on Result #704396

Linear OA(3103, 758, F3, 24) (dual of [758, 655, 25]-code), using construction XX applied to C1 = C([724,18]), C2 = C([0,19]), C3 = C1 + C2 = C([0,18]), and C∩ = C1 ∩ C2 = C([724,19]) based on
  1. linear OA(391, 728, F3, 23) (dual of [728, 637, 24]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {−4,−3,…,18}, and designed minimum distance d ≥ |I|+1 = 24 [i]
  2. linear OA(379, 728, F3, 20) (dual of [728, 649, 21]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [0,19], and designed minimum distance d ≥ |I|+1 = 21 [i]
  3. linear OA(397, 728, F3, 24) (dual of [728, 631, 25]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {−4,−3,…,19}, and designed minimum distance d ≥ |I|+1 = 25 [i]
  4. linear OA(373, 728, F3, 19) (dual of [728, 655, 20]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [0,18], and designed minimum distance d ≥ |I|+1 = 20 [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(3103, 718, F3, 2, 24) (dual of [(718, 2), 1333, 25]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(3103, 718, F3, 3, 24) (dual of [(718, 3), 2051, 25]-NRT-code) [i]
3Linear OOA(3103, 718, F3, 4, 24) (dual of [(718, 4), 2769, 25]-NRT-code) [i]
4Linear OOA(3103, 718, F3, 5, 24) (dual of [(718, 5), 3487, 25]-NRT-code) [i]
5Digital (79, 103, 718)-net over F3 [i]
6Linear OOA(3103, 379, F3, 2, 24) (dual of [(379, 2), 655, 25]-NRT-code) [i]OOA Folding