Information on Result #952654
Linear OOA(3159, 1594333, F3, 3, 17) (dual of [(1594333, 3), 4782840, 18]-NRT-code), using OOA 3-folding based on linear OA(3159, 4782999, F3, 17) (dual of [4782999, 4782840, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(3159, 4783001, F3, 17) (dual of [4783001, 4782842, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(13) [i] based on
- linear OA(3155, 4782969, F3, 17) (dual of [4782969, 4782814, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(3127, 4782969, F3, 14) (dual of [4782969, 4782842, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(34, 32, F3, 2) (dual of [32, 28, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(34, 40, F3, 2) (dual of [40, 36, 3]-code), using
- Hamming code H(4,3) [i]
- discarding factors / shortening the dual code based on linear OA(34, 40, F3, 2) (dual of [40, 36, 3]-code), using
- construction X applied to Ce(16) ⊂ Ce(13) [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(3159, 1506010, F3, 4, 17) (dual of [(1506010, 4), 6023881, 18]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3159, 1506010, F3, 5, 17) (dual of [(1506010, 5), 7529891, 18]-NRT-code) | [i] | ||
| 3 | Digital (142, 159, 1506010)-net over F3 | [i] | ||