Information on Result #952402
Linear OOA(3131, 1594333, F3, 3, 14) (dual of [(1594333, 3), 4782868, 15]-NRT-code), using OOA 3-folding based on linear OA(3131, 4782999, F3, 14) (dual of [4782999, 4782868, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(3131, 4783001, F3, 14) (dual of [4783001, 4782870, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(10) [i] based on
- 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(399, 4782969, F3, 11) (dual of [4782969, 4782870, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [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(13) ⊂ Ce(10) [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(3131, 1594333, F3, 4, 14) (dual of [(1594333, 4), 6377201, 15]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3131, 1594333, F3, 5, 14) (dual of [(1594333, 5), 7971534, 15]-NRT-code) | [i] | ||
| 3 | Digital (117, 131, 1594333)-net over F3 | [i] | ||