Information on Result #731398
Linear OA(980, 13132, F9, 20) (dual of [13132, 13052, 21]-code), using trace code based on linear OA(8140, 6566, F81, 20) (dual of [6566, 6526, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(17) [i] based on
- linear OA(8139, 6561, F81, 20) (dual of [6561, 6522, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(8135, 6561, F81, 18) (dual of [6561, 6526, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(811, 5, F81, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(811, s, F81, 1) (dual of [s, s−1, 2]-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 OA(981, 13133, F9, 20) (dual of [13133, 13052, 21]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(980, 13132, F9, 2, 20) (dual of [(13132, 2), 26184, 21]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(980, 13132, F9, 3, 20) (dual of [(13132, 3), 39316, 21]-NRT-code) | [i] | ||
| 4 | Digital (60, 80, 13132)-net over F9 | [i] | ||
| 5 | Linear OA(981, 13134, F9, 20) (dual of [13134, 13053, 21]-code) | [i] | Construction X with Varšamov Bound | |
| 6 | Linear OOA(980, 6566, F9, 2, 20) (dual of [(6566, 2), 13052, 21]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(980, 4377, F9, 3, 20) (dual of [(4377, 3), 13051, 21]-NRT-code) | [i] | ||
| 8 | Linear OOA(980, 1313, F9, 20, 20) (dual of [(1313, 20), 26180, 21]-NRT-code) | [i] | OA Folding and Stacking | |