Information on Result #2678071
Linear OOA(3232, 177168, F3, 3, 28) (dual of [(177168, 3), 531272, 29]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(3229, 177167, F3, 3, 28) (dual of [(177167, 3), 531272, 29]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3229, 531501, F3, 28) (dual of [531501, 531272, 29]-code), using
- 1 times code embedding in larger space [i] based on linear OA(3228, 531500, F3, 28) (dual of [531500, 531272, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(21) [i] based on
- linear OA(3217, 531441, F3, 28) (dual of [531441, 531224, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [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(311, 59, F3, 5) (dual of [59, 48, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(311, 85, F3, 5) (dual of [85, 74, 6]-code), using
- construction X applied to Ce(27) ⊂ Ce(21) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(3228, 531500, F3, 28) (dual of [531500, 531272, 29]-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(3232, 174907, F3, 4, 28) (dual of [(174907, 4), 699396, 29]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3232, 174907, F3, 5, 28) (dual of [(174907, 5), 874303, 29]-NRT-code) | [i] | ||
| 3 | Digital (204, 232, 174907)-net over F3 | [i] | ||