Information on Result #721317

Linear OA(1620, 89, F16, 11) (dual of [89, 69, 12]-code), using construction XX applied to C1 = C([3,12]), C2 = C([2,11]), C3 = C1 + C2 = C([3,11]), and C∩ = C1 ∩ C2 = C([2,12]) based on
  1. linear OA(1618, 85, F16, 10) (dual of [85, 67, 11]-code), using the BCH-code C(I) with length 85 | 162−1, defining interval I = {3,4,…,12}, and designed minimum distance d ≥ |I|+1 = 11 [i]
  2. linear OA(1618, 85, F16, 10) (dual of [85, 67, 11]-code), using the BCH-code C(I) with length 85 | 162−1, defining interval I = {2,3,…,11}, and designed minimum distance d ≥ |I|+1 = 11 [i]
  3. linear OA(1620, 85, F16, 11) (dual of [85, 65, 12]-code), using the BCH-code C(I) with length 85 | 162−1, defining interval I = {2,3,…,12}, and designed minimum distance d ≥ |I|+1 = 12 [i]
  4. linear OA(1616, 85, F16, 9) (dual of [85, 69, 10]-code), using the BCH-code C(I) with length 85 | 162−1, defining interval I = {3,4,…,11}, and designed minimum distance d ≥ |I|+1 = 10 [i]
  5. linear OA(160, 2, F16, 0) (dual of [2, 2, 1]-code), using
  6. linear OA(160, 2, F16, 0) (dual of [2, 2, 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 OA(16126, 1048670, F16, 23) (dual of [1048670, 1048544, 24]-code) [i](u, u+v)-Construction
2Linear OOA(1620, 89, F16, 2, 11) (dual of [(89, 2), 158, 12]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
3Digital (9, 20, 89)-net over F16 [i]