Information on Result #1080930
Linear OOA(3136, large, F3, 4, 9), using (u, u+v)-construction 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
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(3136, large, F3, 4, 8) | [i] | Strength Reduction for OOAs | |
| 2 | Linear OOA(3136, large, F3, 4, 7) | [i] | ||
| 3 | Linear OOA(3136, large, F3, 4, 6) | [i] | ||
| 4 | Linear OOA(3136, large, F3, 4, 5) | [i] | ||
| 5 | Linear OOA(3136, large, F3, 4, 4) | [i] | ||
| 6 | Linear OOA(3136, large, F3, 4, 3) | [i] | ||
| 7 | Linear OOA(3144, large, F3, 4, 9) | [i] | NRT-Code Embedding in Larger Space | |
| 8 | Linear OOA(3148, large, F3, 4, 9) | [i] | ||
| 9 | Linear OOA(3152, large, F3, 4, 9) | [i] | ||
| 10 | Linear OOA(3160, large, F3, 4, 9) | [i] | ||
| 11 | Linear OOA(3164, large, F3, 4, 9) | [i] | ||
| 12 | Linear OOA(3168, large, F3, 4, 9) | [i] | ||
| 13 | Linear OOA(3176, large, F3, 4, 9) | [i] | ||
| 14 | Linear OOA(3180, large, F3, 4, 9) | [i] | ||
| 15 | Linear OOA(3184, large, F3, 4, 9) | [i] | ||
| 16 | Linear OOA(3192, large, F3, 4, 9) | [i] | ||
| 17 | Linear OOA(3196, large, F3, 4, 9) | [i] | ||
| 18 | Linear OOA(3200, large, F3, 4, 9) | [i] | ||
| 19 | Linear OOA(3208, large, F3, 4, 9) | [i] | ||
| 20 | Linear OOA(3212, large, F3, 4, 9) | [i] | ||
| 21 | Linear OOA(3216, large, F3, 4, 9) | [i] | ||
| 22 | Linear OOA(3224, large, F3, 4, 9) | [i] | ||
| 23 | Linear OOA(3228, large, F3, 4, 9) | [i] | ||
| 24 | Linear OOA(3232, large, F3, 4, 9) | [i] | ||
| 25 | Linear OOA(3240, large, F3, 4, 9) | [i] | ||
| 26 | Linear OOA(3244, large, F3, 4, 9) | [i] | ||
| 27 | Linear OOA(3248, large, F3, 4, 9) | [i] | ||
| 28 | Linear OOA(3137, large, F3, 4, 9) | [i] | OOA Duplication | |
| 29 | Linear OOA(3138, large, F3, 4, 9) | [i] | ||
| 30 | Linear OOA(3139, large, F3, 4, 9) | [i] | ||
| 31 | Linear OOA(3136, 8388602, F3, 5, 9) (dual of [(8388602, 5), 41942874, 10]-NRT-code) | [i] | OOA Stacking with Additional Row | |
| 32 | Linear OOA(3136, 8388602, F3, 12, 9) (dual of [(8388602, 12), 100663088, 10]-NRT-code) | [i] | ||