Information on Result #952334
Linear OOA(3117, 1594333, F3, 3, 13) (dual of [(1594333, 3), 4782882, 14]-NRT-code), using OOA 3-folding based on linear OA(3117, 4782999, F3, 13) (dual of [4782999, 4782882, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(3117, 4783001, F3, 13) (dual of [4783001, 4782884, 14]-code), using
- construction X applied to Ce(12) ⊂ Ce(9) [i] based on
- linear OA(3113, 4782969, F3, 13) (dual of [4782969, 4782856, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(385, 4782969, F3, 10) (dual of [4782969, 4782884, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [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(12) ⊂ Ce(9) [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(3117, 1594333, F3, 4, 13) (dual of [(1594333, 4), 6377215, 14]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3117, 1594333, F3, 5, 13) (dual of [(1594333, 5), 7971548, 14]-NRT-code) | [i] | ||
| 3 | Digital (104, 117, 1594333)-net over F3 | [i] | ||