Information on Result #812678
Linear OOA(372, 2391492, F3, 2, 8) (dual of [(2391492, 2), 4782912, 9]-NRT-code), using OOA 2-folding based on linear OA(372, 4782984, F3, 8) (dual of [4782984, 4782912, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(372, 4782985, F3, 8) (dual of [4782985, 4782913, 9]-code), using
- construction X4 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(315, 16, F3, 15) (dual of [16, 1, 16]-code or 16-arc in PG(14,3)), using
- dual of repetition code with length 16 [i]
- linear OA(31, 16, F3, 1) (dual of [16, 15, 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 X4 applied to Ce(7) ⊂ Ce(6) [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(3101, 4782984, F3, 2, 8) (dual of [(4782984, 2), 9565867, 9]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |
| 2 | Linear OOA(3223, 6585793, F3, 2, 16) (dual of [(6585793, 2), 13171363, 17]-NRT-code) | [i] | ||
| 3 | Linear OOA(3238, 6585793, F3, 2, 17) (dual of [(6585793, 2), 13171348, 18]-NRT-code) | [i] | ||
| 4 | Linear OOA(372, 2391492, F3, 3, 8) (dual of [(2391492, 3), 7174404, 9]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 5 | Linear OOA(372, 2391492, F3, 4, 8) (dual of [(2391492, 4), 9565896, 9]-NRT-code) | [i] | ||
| 6 | Linear OOA(372, 2391492, F3, 5, 8) (dual of [(2391492, 5), 11957388, 9]-NRT-code) | [i] | ||
| 7 | Digital (64, 72, 2391492)-net over F3 | [i] | ||