Information on Result #730147
Linear OA(8139, 412, F81, 22) (dual of [412, 373, 23]-code), using construction X applied to C([30,51]) ⊂ C([31,51]) based on
- linear OA(8139, 410, F81, 22) (dual of [410, 371, 23]-code), using the BCH-code C(I) with length 410 | 812−1, defining interval I = {30,31,…,51}, and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(8137, 410, F81, 21) (dual of [410, 373, 22]-code), using the BCH-code C(I) with length 410 | 812−1, defining interval I = {31,32,…,51}, and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(810, 2, F81, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(810, s, F81, 0) (dual of [s, s, 1]-code) for arbitrarily large s, 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:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(8139, 412, F81, 2, 22) (dual of [(412, 2), 785, 23]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(8139, 412, F81, 3, 22) (dual of [(412, 3), 1197, 23]-NRT-code) | [i] | ||
| 3 | Linear OOA(8139, 412, F81, 4, 22) (dual of [(412, 4), 1609, 23]-NRT-code) | [i] | ||
| 4 | Digital (17, 39, 412)-net over F81 | [i] | ||
| 5 | Linear OA(8140, 480, F81, 22) (dual of [480, 440, 23]-code) | [i] | Varšamov–Edel Lengthening | |
| 6 | Linear OOA(8139, 206, F81, 2, 22) (dual of [(206, 2), 373, 23]-NRT-code) | [i] | OOA Folding | |