Information on Result #712739

Linear OA(727, 177, F7, 11) (dual of [177, 150, 12]-code), using construction XX applied to C1 = C([24,33]), C2 = C([23,32]), C3 = C1 + C2 = C([24,32]), and C∩ = C1 ∩ C2 = C([23,33]) based on
  1. linear OA(724, 171, F7, 10) (dual of [171, 147, 11]-code), using the BCH-code C(I) with length 171 | 73−1, defining interval I = {24,25,…,33}, and designed minimum distance d ≥ |I|+1 = 11 [i]
  2. linear OA(724, 171, F7, 10) (dual of [171, 147, 11]-code), using the BCH-code C(I) with length 171 | 73−1, defining interval I = {23,24,…,32}, and designed minimum distance d ≥ |I|+1 = 11 [i]
  3. linear OA(727, 171, F7, 11) (dual of [171, 144, 12]-code), using the BCH-code C(I) with length 171 | 73−1, defining interval I = {23,24,…,33}, and designed minimum distance d ≥ |I|+1 = 12 [i]
  4. linear OA(721, 171, F7, 9) (dual of [171, 150, 10]-code), using the BCH-code C(I) with length 171 | 73−1, defining interval I = {24,25,…,32}, and designed minimum distance d ≥ |I|+1 = 10 [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(727, 177, F7, 2, 11) (dual of [(177, 2), 327, 12]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(727, 177, F7, 3, 11) (dual of [(177, 3), 504, 12]-NRT-code) [i]
3Digital (16, 27, 177)-net over F7 [i]
4Linear OOA(727, 88, F7, 2, 11) (dual of [(88, 2), 149, 12]-NRT-code) [i]OOA Folding
5Linear OOA(727, 59, F7, 3, 11) (dual of [(59, 3), 150, 12]-NRT-code) [i]