Information on Result #812948
Linear OOA(3114, 2391499, F3, 2, 12) (dual of [(2391499, 2), 4782884, 13]-NRT-code), using OOA 2-folding based on linear OA(3114, 4782998, F3, 12) (dual of [4782998, 4782884, 13]-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(31, 29, F3, 1) (dual of [29, 28, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, 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(3114, 1795678, F3, 3, 12) (dual of [(1795678, 3), 5386920, 13]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3114, 1795678, F3, 4, 12) (dual of [(1795678, 4), 7182598, 13]-NRT-code) | [i] | ||
| 3 | Linear OOA(3114, 1795678, F3, 5, 12) (dual of [(1795678, 5), 8978276, 13]-NRT-code) | [i] | ||
| 4 | Digital (102, 114, 1795678)-net over F3 | [i] | ||