Information on Result #895023
Linear OOA(3127, 4194308, F3, 2, 12) (dual of [(4194308, 2), 8388489, 13]-NRT-code), using (u, u+v)-construction based on
- linear OOA(37, 7, F3, 2, 6) (dual of [(7, 2), 7, 7]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(2;F,7P) [i] based on function field F/F3 with g(F) = 1 and N(F) ≥ 7, using
- linear OOA(3120, 4194301, F3, 2, 12) (dual of [(4194301, 2), 8388482, 13]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3120, 8388602, F3, 12) (dual of [8388602, 8388482, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(3120, large, F3, 12) (dual of [large, large−120, 13]-code), using
- the primitive narrow-sense BCH-code C(I) with length 14348906 = 315−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- discarding factors / shortening the dual code based on linear OA(3120, large, F3, 12) (dual of [large, large−120, 13]-code), using
- OOA 2-folding [i] based on linear OA(3120, 8388602, F3, 12) (dual of [8388602, 8388482, 13]-code), using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, k and s, k and t, m and s, m 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(3127, 4194308, F3, 3, 12) (dual of [(4194308, 3), 12582797, 13]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3127, 4194308, F3, 4, 12) (dual of [(4194308, 4), 16777105, 13]-NRT-code) | [i] | ||
| 3 | Linear OOA(3127, 4194308, F3, 5, 12) (dual of [(4194308, 5), 20971413, 13]-NRT-code) | [i] | ||
| 4 | Digital (115, 127, 4194308)-net over F3 | [i] | ||
| 5 | Linear OOA(3127, 2097154, F3, 4, 12) (dual of [(2097154, 4), 8388489, 13]-NRT-code) | [i] | OOA Folding | |