Information on Result #731342
Linear OA(934, 13126, F9, 9) (dual of [13126, 13092, 10]-code), using trace code based on linear OA(8117, 6563, F81, 9) (dual of [6563, 6546, 10]-code), using
- construction X applied to Ce(8) ⊂ Ce(7) [i] based on
- linear OA(8117, 6561, F81, 9) (dual of [6561, 6544, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(8115, 6561, F81, 8) (dual of [6561, 6546, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [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 OA(935, 13127, F9, 9) (dual of [13127, 13092, 10]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(939, 13142, F9, 9) (dual of [13142, 13103, 10]-code) | [i] | (u, u+v)-Construction | |
| 3 | Linear OA(939, 13146, F9, 9) (dual of [13146, 13107, 10]-code) | [i] | ||
| 4 | Linear OOA(934, 13126, F9, 2, 9) (dual of [(13126, 2), 26218, 10]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 5 | Linear OOA(934, 13126, F9, 3, 9) (dual of [(13126, 3), 39344, 10]-NRT-code) | [i] | ||
| 6 | Digital (25, 34, 13126)-net over F9 | [i] | ||
| 7 | Linear OA(935, 13128, F9, 9) (dual of [13128, 13093, 10]-code) | [i] | Construction X with Varšamov Bound | |
| 8 | Linear OOA(934, 6563, F9, 2, 9) (dual of [(6563, 2), 13092, 10]-NRT-code) | [i] | OOA Folding | |
| 9 | Linear OOA(934, 4375, F9, 3, 9) (dual of [(4375, 3), 13091, 10]-NRT-code) | [i] | ||
| 10 | Linear OOA(934, 3281, F9, 9, 9) (dual of [(3281, 9), 29495, 10]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |