Information on Result #704642

Linear OA(3137, 757, F3, 33) (dual of [757, 620, 34]-code), using construction XX applied to C1 = C([724,27]), C2 = C([1,28]), C3 = C1 + C2 = C([1,27]), and C∩ = C1 ∩ C2 = C([724,28]) 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(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(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(30, 3, F3, 0) (dual of [3, 3, 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(3137, 742, F3, 2, 33) (dual of [(742, 2), 1347, 34]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(3137, 742, F3, 3, 33) (dual of [(742, 3), 2089, 34]-NRT-code) [i]
3Linear OOA(3137, 742, F3, 4, 33) (dual of [(742, 4), 2831, 34]-NRT-code) [i]
4Linear OOA(3137, 742, F3, 5, 33) (dual of [(742, 5), 3573, 34]-NRT-code) [i]
5Digital (104, 137, 742)-net over F3 [i]