Information on Result #712733

Linear OA(715, 177, F7, 6) (dual of [177, 162, 7]-code), using construction XX applied to C1 = C([25,29]), C2 = C([24,28]), C3 = C1 + C2 = C([25,28]), and C∩ = C1 ∩ C2 = C([24,29]) based on
  1. linear OA(712, 171, F7, 5) (dual of [171, 159, 6]-code), using the BCH-code C(I) with length 171 | 73−1, defining interval I = {25,26,27,28,29}, and designed minimum distance d ≥ |I|+1 = 6 [i]
  2. linear OA(712, 171, F7, 5) (dual of [171, 159, 6]-code), using the BCH-code C(I) with length 171 | 73−1, defining interval I = {24,25,26,27,28}, and designed minimum distance d ≥ |I|+1 = 6 [i]
  3. linear OA(715, 171, F7, 6) (dual of [171, 156, 7]-code), using the BCH-code C(I) with length 171 | 73−1, defining interval I = {24,25,…,29}, and designed minimum distance d ≥ |I|+1 = 7 [i]
  4. linear OA(79, 171, F7, 4) (dual of [171, 162, 5]-code), using the BCH-code C(I) with length 171 | 73−1, defining interval I = {25,26,27,28}, and designed minimum distance d ≥ |I|+1 = 5 [i]
  5. linear OA(70, 3, F7, 0) (dual of [3, 3, 1]-code), using
  6. linear OA(70, 3, F7, 0) (dual of [3, 3, 1]-code) (see above)

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(715, 177, F7, 2, 6) (dual of [(177, 2), 339, 7]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(715, 177, F7, 3, 6) (dual of [(177, 3), 516, 7]-NRT-code) [i]
3Digital (9, 15, 177)-net over F7 [i]
4Linear OOA(715, 88, F7, 2, 6) (dual of [(88, 2), 161, 7]-NRT-code) [i]OOA Folding
5Linear OOA(715, 59, F7, 3, 6) (dual of [(59, 3), 162, 7]-NRT-code) [i]