Information on Result #704827

Linear OA(3148, 758, F3, 36) (dual of [758, 610, 37]-code), using construction XX applied to C1 = C([724,30]), C2 = C([0,31]), C3 = C1 + C2 = C([0,30]), and C∩ = C1 ∩ C2 = C([724,31]) based on
  1. linear OA(3136, 728, F3, 35) (dual of [728, 592, 36]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {−4,−3,…,30}, and designed minimum distance d ≥ |I|+1 = 36 [i]
  2. linear OA(3124, 728, F3, 32) (dual of [728, 604, 33]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [0,31], and designed minimum distance d ≥ |I|+1 = 33 [i]
  3. linear OA(3142, 728, F3, 36) (dual of [728, 586, 37]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {−4,−3,…,31}, and designed minimum distance d ≥ |I|+1 = 37 [i]
  4. linear OA(3118, 728, F3, 31) (dual of [728, 610, 32]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [0,30], and designed minimum distance d ≥ |I|+1 = 32 [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(3148, 752, F3, 2, 36) (dual of [(752, 2), 1356, 37]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(3148, 752, F3, 3, 36) (dual of [(752, 3), 2108, 37]-NRT-code) [i]
3Linear OOA(3148, 752, F3, 4, 36) (dual of [(752, 4), 2860, 37]-NRT-code) [i]
4Linear OOA(3148, 752, F3, 5, 36) (dual of [(752, 5), 3612, 37]-NRT-code) [i]
5Digital (112, 148, 752)-net over F3 [i]
6Linear OOA(3148, 379, F3, 2, 36) (dual of [(379, 2), 610, 37]-NRT-code) [i]OOA Folding