Information on Result #812680
Linear OOA(375, 2391500, F3, 2, 8) (dual of [(2391500, 2), 4782925, 9]-NRT-code), using OOA 2-folding based on linear OA(375, 4783000, F3, 8) (dual of [4783000, 4782925, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(375, 4783001, F3, 8) (dual of [4783001, 4782926, 9]-code), using
- construction X applied to Ce(7) ⊂ Ce(4) [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(343, 4782969, F3, 5) (dual of [4782969, 4782926, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(34, 32, F3, 2) (dual of [32, 28, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(34, 40, F3, 2) (dual of [40, 36, 3]-code), using
- Hamming code H(4,3) [i]
- discarding factors / shortening the dual code based on linear OA(34, 40, F3, 2) (dual of [40, 36, 3]-code), using
- construction X applied to Ce(7) ⊂ Ce(4) [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(3104, 4783000, F3, 2, 8) (dual of [(4783000, 2), 9565896, 9]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |
| 2 | Linear OOA(3241, 6585801, F3, 2, 17) (dual of [(6585801, 2), 13171361, 18]-NRT-code) | [i] | ||
| 3 | Linear OOA(375, 2391500, F3, 3, 8) (dual of [(2391500, 3), 7174425, 9]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(375, 2391500, F3, 4, 8) (dual of [(2391500, 4), 9565925, 9]-NRT-code) | [i] | ||
| 5 | Linear OOA(375, 2391500, F3, 5, 8) (dual of [(2391500, 5), 11957425, 9]-NRT-code) | [i] | ||
| 6 | Digital (67, 75, 2391500)-net over F3 | [i] | ||