Information on Result #1303094
Linear OA(931, 13128, F9, 8) (dual of [13128, 13097, 9]-code), using construction X with Varšamov bound based on
- linear OA(930, 13126, F9, 8) (dual of [13126, 13096, 9]-code), using
- trace code [i] based on linear OA(8115, 6563, F81, 8) (dual of [6563, 6548, 9]-code), using
- construction X applied to Ce(7) ⊂ Ce(6) [i] based on
- 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(8113, 6561, F81, 7) (dual of [6561, 6548, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [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(7) ⊂ Ce(6) [i] based on
- trace code [i] based on linear OA(8115, 6563, F81, 8) (dual of [6563, 6548, 9]-code), using
- linear OA(930, 13127, F9, 7) (dual of [13127, 13097, 8]-code), using Gilbert–Varšamov bound and bm = 930 > Vbs−1(k−1) = 1860 074255 197268 143189 569009 [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(931, 13128, F9, 2, 8) (dual of [(13128, 2), 26225, 9]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(931, 13128, F9, 3, 8) (dual of [(13128, 3), 39353, 9]-NRT-code) | [i] | ||
| 3 | Digital (23, 31, 13128)-net over F9 | [i] | ||
| 4 | Linear OOA(931, 6564, F9, 2, 8) (dual of [(6564, 2), 13097, 9]-NRT-code) | [i] | OOA Folding | |