Information on Result #731424
Linear OA(996, 13132, F9, 24) (dual of [13132, 13036, 25]-code), using trace code based on linear OA(8148, 6566, F81, 24) (dual of [6566, 6518, 25]-code), using
- construction X applied to Ce(23) ⊂ Ce(21) [i] based on
- linear OA(8147, 6561, F81, 24) (dual of [6561, 6514, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(8143, 6561, F81, 22) (dual of [6561, 6518, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [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(997, 13133, F9, 24) (dual of [13133, 13036, 25]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(996, 13132, F9, 2, 24) (dual of [(13132, 2), 26168, 25]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(996, 13132, F9, 3, 24) (dual of [(13132, 3), 39300, 25]-NRT-code) | [i] | ||
| 4 | Digital (72, 96, 13132)-net over F9 | [i] | ||
| 5 | Linear OA(997, 13134, F9, 24) (dual of [13134, 13037, 25]-code) | [i] | Construction X with Varšamov Bound | |
| 6 | Linear OOA(996, 6566, F9, 2, 24) (dual of [(6566, 2), 13036, 25]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(996, 4377, F9, 3, 24) (dual of [(4377, 3), 13035, 25]-NRT-code) | [i] | ||
| 8 | Linear OOA(996, 1094, F9, 24, 24) (dual of [(1094, 24), 26160, 25]-NRT-code) | [i] | OA Folding and Stacking | |