Information on Result #2487289
Linear OOA(3174, 9847, F3, 2, 29) (dual of [(9847, 2), 19520, 30]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(3172, 9846, F3, 2, 29) (dual of [(9846, 2), 19520, 30]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3172, 19692, F3, 29) (dual of [19692, 19520, 30]-code), using
- construction X applied to Ce(28) ⊂ Ce(27) [i] based on
- linear OA(3172, 19683, F3, 29) (dual of [19683, 19511, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(3163, 19683, F3, 28) (dual of [19683, 19520, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(30, 9, F3, 0) (dual of [9, 9, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(30, s, F3, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(28) ⊂ Ce(27) [i] based on
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(3174, 7536, F3, 3, 29) (dual of [(7536, 3), 22434, 30]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3174, 7536, F3, 4, 29) (dual of [(7536, 4), 29970, 30]-NRT-code) | [i] | ||
| 3 | Linear OOA(3174, 7536, F3, 5, 29) (dual of [(7536, 5), 37506, 30]-NRT-code) | [i] | ||
| 4 | Digital (145, 174, 7536)-net over F3 | [i] | ||