Information on Result #952755
Linear OOA(3169, 1594327, F3, 3, 18) (dual of [(1594327, 3), 4782812, 19]-NRT-code), using OOA 3-folding based on linear OA(3169, 4782981, F3, 18) (dual of [4782981, 4782812, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(3169, 4782983, F3, 18) (dual of [4782983, 4782814, 19]-code), using
- 1 times truncation [i] based on linear OA(3170, 4782984, F3, 19) (dual of [4782984, 4782814, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(16) [i] based on
- linear OA(3169, 4782969, F3, 19) (dual of [4782969, 4782800, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(3155, 4782969, F3, 17) (dual of [4782969, 4782814, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [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(18) ⊂ Ce(16) [i] based on
- 1 times truncation [i] based on linear OA(3170, 4782984, F3, 19) (dual of [4782984, 4782814, 20]-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(3169, 1373152, F3, 4, 18) (dual of [(1373152, 4), 5492439, 19]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3169, 1373152, F3, 5, 18) (dual of [(1373152, 5), 6865591, 19]-NRT-code) | [i] | ||
| 3 | Digital (151, 169, 1373152)-net over F3 | [i] | ||