Information on Result #1303086
Linear OA(923, 13128, F9, 6) (dual of [13128, 13105, 7]-code), using construction X with Varšamov bound based on
- linear OA(922, 13126, F9, 6) (dual of [13126, 13104, 7]-code), using
- trace code [i] based on linear OA(8111, 6563, F81, 6) (dual of [6563, 6552, 7]-code), using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- linear OA(8111, 6561, F81, 6) (dual of [6561, 6550, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(819, 6561, F81, 5) (dual of [6561, 6552, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [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(5) ⊂ Ce(4) [i] based on
- trace code [i] based on linear OA(8111, 6563, F81, 6) (dual of [6563, 6552, 7]-code), using
- linear OA(922, 13127, F9, 5) (dual of [13127, 13105, 6]-code), using Gilbert–Varšamov bound and bm = 922 > Vbs−1(k−1) = 5 064030 538616 385009 [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(923, 13128, F9, 2, 6) (dual of [(13128, 2), 26233, 7]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(923, 13128, F9, 3, 6) (dual of [(13128, 3), 39361, 7]-NRT-code) | [i] | ||
| 3 | Digital (17, 23, 13128)-net over F9 | [i] | ||
| 4 | Linear OOA(923, 6564, F9, 2, 6) (dual of [(6564, 2), 13105, 7]-NRT-code) | [i] | OOA Folding | |