Information on Result #712829

Linear OA(781, 189, F7, 34) (dual of [189, 108, 35]-code), using construction XX applied to C1 = C([168,28]), C2 = C([1,30]), C3 = C1 + C2 = C([1,28]), and C∩ = C1 ∩ C2 = C([168,30]) based on
  1. linear OA(770, 171, F7, 32) (dual of [171, 101, 33]-code), using the BCH-code C(I) with length 171 | 73−1, defining interval I = {−3,−2,…,28}, and designed minimum distance d ≥ |I|+1 = 33 [i]
  2. linear OA(769, 171, F7, 30) (dual of [171, 102, 31]-code), using the narrow-sense BCH-code C(I) with length 171 | 73−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
  3. linear OA(776, 171, F7, 34) (dual of [171, 95, 35]-code), using the BCH-code C(I) with length 171 | 73−1, defining interval I = {−3,−2,…,30}, and designed minimum distance d ≥ |I|+1 = 35 [i]
  4. linear OA(763, 171, F7, 28) (dual of [171, 108, 29]-code), using the narrow-sense BCH-code C(I) with length 171 | 73−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
  5. linear OA(74, 11, F7, 3) (dual of [11, 7, 4]-code or 11-cap in PG(3,7)), using
  6. linear OA(71, 7, F7, 1) (dual of [7, 6, 2]-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 OA(781, 189, F7, 33) (dual of [189, 108, 34]-code) [i]Strength Reduction
2Linear OA(783, 191, F7, 34) (dual of [191, 108, 35]-code) [i]Code Embedding in Larger Space
3Linear OA(784, 192, F7, 34) (dual of [192, 108, 35]-code) [i]
4Linear OA(780, 188, F7, 33) (dual of [188, 108, 34]-code) [i]Truncation
5Linear OOA(781, 63, F7, 3, 34) (dual of [(63, 3), 108, 35]-NRT-code) [i]OOA Folding