Information on Result #2797285
Linear OOA(3176, large, F3, 4, 9), using 10 times NRT-code embedding in larger space based on linear OOA(3136, large, F3, 4, 9), using
- (u, u+v)-construction [i] based on
- linear OOA(34, 4, F3, 4, 4) (dual of [(4, 4), 12, 5]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(4;12,3) [i]
- linear OOA(3132, 8388600, F3, 4, 9) (dual of [(8388600, 4), 33554268, 10]-NRT-code), using
- trace code [i] based on linear OOA(8133, 2097150, F81, 4, 9) (dual of [(2097150, 4), 8388567, 10]-NRT-code), using
- OOA 4-folding [i] based on linear OA(8133, 8388600, F81, 9) (dual of [8388600, 8388567, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(8133, large, F81, 9) (dual of [large, large−33, 10]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523361 | 818−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(8133, large, F81, 9) (dual of [large, large−33, 10]-code), using
- OOA 4-folding [i] based on linear OA(8133, 8388600, F81, 9) (dual of [8388600, 8388567, 10]-code), using
- trace code [i] based on linear OOA(8133, 2097150, F81, 4, 9) (dual of [(2097150, 4), 8388567, 10]-NRT-code), using
- linear OOA(34, 4, F3, 4, 4) (dual of [(4, 4), 12, 5]-NRT-code), using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, k and t, 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(3177, large, F3, 4, 9) | [i] | OOA Duplication | |
| 2 | Linear OOA(3178, large, F3, 4, 9) | [i] | ||
| 3 | Linear OOA(3179, large, F3, 4, 9) | [i] | ||