Information on Result #1361870
Linear OOA(374, 2391494, F3, 2, 8) (dual of [(2391494, 2), 4782914, 9]-NRT-code), using OOA 2-folding based on linear OA(374, 4782988, F3, 8) (dual of [4782988, 4782914, 9]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(371, 4782983, F3, 8) (dual of [4782983, 4782912, 9]-code), using
- construction X applied to Ce(7) ⊂ Ce(6) [i] based on
- linear OA(371, 4782969, F3, 8) (dual of [4782969, 4782898, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(357, 4782969, F3, 7) (dual of [4782969, 4782912, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [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(7) ⊂ Ce(6) [i] based on
- linear OA(371, 4782985, F3, 6) (dual of [4782985, 4782914, 7]-code), using Gilbert–Varšamov bound and bm = 371 > Vbs−1(k−1) = 667 517554 975509 645021 855027 463073 [i]
- linear OA(31, 3, F3, 1) (dual of [3, 2, 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
- linear OA(371, 4782983, F3, 8) (dual of [4782983, 4782912, 9]-code), using
Mode: 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(374, 2391494, F3, 3, 8) (dual of [(2391494, 3), 7174408, 9]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(374, 2391494, F3, 4, 8) (dual of [(2391494, 4), 9565902, 9]-NRT-code) | [i] | ||
| 3 | Linear OOA(374, 2391494, F3, 5, 8) (dual of [(2391494, 5), 11957396, 9]-NRT-code) | [i] | ||
| 4 | Digital (66, 74, 2391494)-net over F3 | [i] | ||