Information on Result #2677882
Linear OOA(3215, 177162, F3, 3, 26) (dual of [(177162, 3), 531271, 27]-NRT-code), using 31 times duplication based on linear OOA(3214, 177162, F3, 3, 26) (dual of [(177162, 3), 531272, 27]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(3211, 177161, F3, 3, 26) (dual of [(177161, 3), 531272, 27]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3211, 531483, F3, 26) (dual of [531483, 531272, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(21) [i] based on
- linear OA(3205, 531441, F3, 26) (dual of [531441, 531236, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(3169, 531441, F3, 22) (dual of [531441, 531272, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(36, 42, F3, 3) (dual of [42, 36, 4]-code or 42-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
- construction X applied to Ce(25) ⊂ Ce(21) [i] based on
- OOA 3-folding [i] based on linear OA(3211, 531483, F3, 26) (dual of [531483, 531272, 27]-code), 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(3215, 177162, F3, 4, 26) (dual of [(177162, 4), 708433, 27]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3215, 177162, F3, 5, 26) (dual of [(177162, 5), 885595, 27]-NRT-code) | [i] | ||
| 3 | Digital (189, 215, 177162)-net over F3 | [i] | ||