Information on Result #813368
Linear OOA(3128, 88593, F3, 2, 17) (dual of [(88593, 2), 177058, 18]-NRT-code), using OOA 2-folding based on linear OA(3128, 177186, F3, 17) (dual of [177186, 177058, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(12) [i] based on
- linear OA(3122, 177147, F3, 17) (dual of [177147, 177025, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(389, 177147, F3, 13) (dual of [177147, 177058, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(36, 39, F3, 3) (dual of [39, 33, 4]-code or 39-cap in PG(5,3)), using
- discarding factors / shortening the dual code based on linear OA(36, 48, F3, 3) (dual of [48, 42, 4]-code or 48-cap in PG(5,3)), 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 OOA(3130, 88594, F3, 2, 17) (dual of [(88594, 2), 177058, 18]-NRT-code) | [i] | NRT-Code Embedding in Larger Space | |
| 2 | Linear OOA(3132, 88595, F3, 2, 17) (dual of [(88595, 2), 177058, 18]-NRT-code) | [i] | ||
| 3 | Linear OOA(3129, 88593, F3, 2, 17) (dual of [(88593, 2), 177057, 18]-NRT-code) | [i] | OOA Duplication | |
| 4 | Linear OOA(3128, 59487, F3, 3, 17) (dual of [(59487, 3), 178333, 18]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 5 | Linear OOA(3128, 59487, F3, 4, 17) (dual of [(59487, 4), 237820, 18]-NRT-code) | [i] | ||
| 6 | Linear OOA(3128, 59487, F3, 5, 17) (dual of [(59487, 5), 297307, 18]-NRT-code) | [i] | ||
| 7 | Digital (111, 128, 59487)-net over F3 | [i] | ||