Information on Result #704790

Linear OA(3154, 774, F3, 36) (dual of [774, 620, 37]-code), using construction XX applied to C1 = C([724,27]), C2 = C([1,31]), C3 = C1 + C2 = C([1,27]), and C∩ = C1 ∩ C2 = C([724,31]) based on
  1. linear OA(3127, 728, F3, 32) (dual of [728, 601, 33]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {−4,−3,…,27}, and designed minimum distance d ≥ |I|+1 = 33 [i]
  2. linear OA(3123, 728, F3, 31) (dual of [728, 605, 32]-code), using the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,31], and designed minimum distance d ≥ |I|+1 = 32 [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(3108, 728, F3, 27) (dual of [728, 620, 28]-code), using the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [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 OOA(3154, 387, F3, 2, 36) (dual of [(387, 2), 620, 37]-NRT-code) [i]OOA Folding
2Linear OOA(3154, 258, F3, 3, 36) (dual of [(258, 3), 620, 37]-NRT-code) [i]