Information on Result #731456
Linear OA(9110, 13126, F9, 28) (dual of [13126, 13016, 29]-code), using trace code based on linear OA(8155, 6563, F81, 28) (dual of [6563, 6508, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(26) [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(8153, 6561, F81, 27) (dual of [6561, 6508, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [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(9111, 13127, F9, 28) (dual of [13127, 13016, 29]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(9110, 13126, F9, 2, 28) (dual of [(13126, 2), 26142, 29]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(9110, 13126, F9, 3, 28) (dual of [(13126, 3), 39268, 29]-NRT-code) | [i] | ||
| 4 | Digital (82, 110, 13126)-net over F9 | [i] | ||
| 5 | Linear OA(9111, 13128, F9, 28) (dual of [13128, 13017, 29]-code) | [i] | Construction X with Varšamov Bound | |
| 6 | Linear OOA(9110, 6563, F9, 2, 28) (dual of [(6563, 2), 13016, 29]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(9110, 4375, F9, 3, 28) (dual of [(4375, 3), 13015, 29]-NRT-code) | [i] | ||