Information on Result #731460
Linear OA(9112, 13132, F9, 28) (dual of [13132, 13020, 29]-code), using trace code based on linear OA(8156, 6566, F81, 28) (dual of [6566, 6510, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(25) [i] based on
- linear OA(8155, 6561, F81, 28) (dual of [6561, 6506, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(8151, 6561, F81, 26) (dual of [6561, 6510, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [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(9113, 13133, F9, 28) (dual of [13133, 13020, 29]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(9112, 13132, F9, 2, 28) (dual of [(13132, 2), 26152, 29]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(9112, 13132, F9, 3, 28) (dual of [(13132, 3), 39284, 29]-NRT-code) | [i] | ||
| 4 | Digital (84, 112, 13132)-net over F9 | [i] | ||
| 5 | Linear OOA(9112, 6566, F9, 2, 28) (dual of [(6566, 2), 13020, 29]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(9112, 4377, F9, 3, 28) (dual of [(4377, 3), 13019, 29]-NRT-code) | [i] | ||
| 7 | Linear OOA(9112, 938, F9, 28, 28) (dual of [(938, 28), 26152, 29]-NRT-code) | [i] | OA Folding and Stacking | |