Information on Result #730123

Linear OA(8133, 332, F81, 19) (dual of [332, 299, 20]-code), using construction XX applied to C1 = C([33,50]), C2 = C([32,49]), C3 = C1 + C2 = C([33,49]), and C∩ = C1 ∩ C2 = C([32,50]) based on
  1. linear OA(8131, 328, F81, 18) (dual of [328, 297, 19]-code), using the BCH-code C(I) with length 328 | 812−1, defining interval I = {33,34,…,50}, and designed minimum distance d ≥ |I|+1 = 19 [i]
  2. linear OA(8131, 328, F81, 18) (dual of [328, 297, 19]-code), using the BCH-code C(I) with length 328 | 812−1, defining interval I = {32,33,…,49}, and designed minimum distance d ≥ |I|+1 = 19 [i]
  3. linear OA(8133, 328, F81, 19) (dual of [328, 295, 20]-code), using the BCH-code C(I) with length 328 | 812−1, defining interval I = {32,33,…,50}, and designed minimum distance d ≥ |I|+1 = 20 [i]
  4. linear OA(8129, 328, F81, 17) (dual of [328, 299, 18]-code), using the BCH-code C(I) with length 328 | 812−1, defining interval I = {33,34,…,49}, and designed minimum distance d ≥ |I|+1 = 18 [i]
  5. linear OA(810, 2, F81, 0) (dual of [2, 2, 1]-code), using
  6. linear OA(810, 2, F81, 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 OOA(8133, 332, F81, 2, 19) (dual of [(332, 2), 631, 20]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(8133, 332, F81, 3, 19) (dual of [(332, 3), 963, 20]-NRT-code) [i]
3Linear OOA(8133, 332, F81, 4, 19) (dual of [(332, 4), 1295, 20]-NRT-code) [i]
4Digital (14, 33, 332)-net over F81 [i]
5Linear OOA(8133, 166, F81, 2, 19) (dual of [(166, 2), 299, 20]-NRT-code) [i]OOA Folding