Information on Result #952399
Linear OOA(3127, 1594327, F3, 3, 14) (dual of [(1594327, 3), 4782854, 15]-NRT-code), using OOA 3-folding based on linear OA(3127, 4782981, F3, 14) (dual of [4782981, 4782854, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(3127, 4782983, F3, 14) (dual of [4782983, 4782856, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(12) [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(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(30, 14, F3, 0) (dual of [14, 14, 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(13) ⊂ Ce(12) [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(3127, 1594327, F3, 4, 14) (dual of [(1594327, 4), 6377181, 15]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3127, 1594327, F3, 5, 14) (dual of [(1594327, 5), 7971508, 15]-NRT-code) | [i] | ||
| 3 | Digital (113, 127, 1594327)-net over F3 | [i] | ||