Information on Result #1303398
Linear OA(9111, 13128, F9, 28) (dual of [13128, 13017, 29]-code), using construction X with Varšamov bound based on
- linear OA(9110, 13126, F9, 28) (dual of [13126, 13016, 29]-code), using
- trace code [i] 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
- construction X applied to Ce(27) ⊂ Ce(26) [i] based on
- trace code [i] based on linear OA(8155, 6563, F81, 28) (dual of [6563, 6508, 29]-code), using
- linear OA(9110, 13127, F9, 27) (dual of [13127, 13017, 28]-code), using Gilbert–Varšamov bound and bm = 9110 > Vbs−1(k−1) = 86 200676 142235 012215 619549 199577 703251 856613 280998 578887 011642 182925 923461 766876 807866 643992 501811 981809 [i]
- linear OA(90, 1, F9, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(90, s, F9, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
Mode: 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 OOA(9111, 13128, F9, 2, 28) (dual of [(13128, 2), 26145, 29]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(9111, 13128, F9, 3, 28) (dual of [(13128, 3), 39273, 29]-NRT-code) | [i] | ||
| 3 | Digital (83, 111, 13128)-net over F9 | [i] | ||
| 4 | Linear OOA(9111, 6564, F9, 2, 28) (dual of [(6564, 2), 13017, 29]-NRT-code) | [i] | OOA Folding | |