Information on Result #704635

Linear OA(3142, 774, F3, 33) (dual of [774, 632, 34]-code), using construction XX applied to C1 = C([724,24]), C2 = C([1,28]), C3 = C1 + C2 = C([1,24]), and C∩ = C1 ∩ C2 = C([724,28]) based on
  1. linear OA(3115, 728, F3, 29) (dual of [728, 613, 30]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {−4,−3,…,24}, and designed minimum distance d ≥ |I|+1 = 30 [i]
  2. linear OA(3111, 728, F3, 28) (dual of [728, 617, 29]-code), using the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
  3. linear OA(3130, 728, F3, 33) (dual of [728, 598, 34]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {−4,−3,…,28}, and designed minimum distance d ≥ |I|+1 = 34 [i]
  4. linear OA(396, 728, F3, 24) (dual of [728, 632, 25]-code), using the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
  5. linear OA(37, 26, F3, 4) (dual of [26, 19, 5]-code), using
    • the primitive expurgated narrow-sense BCH-code C(I) with length 26 = 33−1, defining interval I = [0,2], and designed minimum distance d ≥ |I|+1 = 5 [i]
  6. linear OA(35, 20, F3, 3) (dual of [20, 15, 4]-code or 20-cap in PG(4,3)), 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 OA(3143, 775, F3, 33) (dual of [775, 632, 34]-code) [i]Code Embedding in Larger Space
2Linear OOA(3142, 387, F3, 2, 33) (dual of [(387, 2), 632, 34]-NRT-code) [i]OOA Folding
3Linear OOA(3142, 258, F3, 3, 33) (dual of [(258, 3), 632, 34]-NRT-code) [i]