Information on Result #1060826
Linear OOA(3197, 1195745, F3, 4, 21) (dual of [(1195745, 4), 4782783, 22]-NRT-code), using OOA 4-folding based on linear OA(3197, 4782980, F3, 21) (dual of [4782980, 4782783, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(3197, 4782983, F3, 21) (dual of [4782983, 4782786, 22]-code), using
- 1 times truncation [i] based on linear OA(3198, 4782984, F3, 22) (dual of [4782984, 4782786, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(19) [i] based on
- linear OA(3197, 4782969, F3, 22) (dual of [4782969, 4782772, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(3183, 4782969, F3, 20) (dual of [4782969, 4782786, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(31, 15, F3, 1) (dual of [15, 14, 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
- construction X applied to Ce(21) ⊂ Ce(19) [i] based on
- 1 times truncation [i] based on linear OA(3198, 4782984, F3, 22) (dual of [4782984, 4782786, 23]-code), 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(3197, 1195745, F3, 5, 21) (dual of [(1195745, 5), 5978528, 22]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (176, 197, 1195745)-net over F3 | [i] | ||