Information on Result #1014248
Linear OOA(862, large, F8, 3, 7), using (u, u+v)-construction based on
- linear OOA(812, 2931457, F8, 3, 3) (dual of [(2931457, 3), 8794359, 4]-NRT-code), using
- appending kth column [i] based on linear OOA(812, 2931457, F8, 2, 3) (dual of [(2931457, 2), 5862902, 4]-NRT-code), using
- OAs with strength 3, b ≠ 2, and m > 3 are always embeddable [i] based on linear OA(812, 2931457, F8, 3) (dual of [2931457, 2931445, 4]-code or 2931457-cap in PG(11,8)), using
- appending kth column [i] based on linear OOA(812, 2931457, F8, 2, 3) (dual of [(2931457, 2), 5862902, 4]-NRT-code), using
- linear OOA(850, 5592402, F8, 3, 7) (dual of [(5592402, 3), 16777156, 8]-NRT-code), using
- trace code [i] based on linear OOA(6425, 2796201, F64, 3, 7) (dual of [(2796201, 3), 8388578, 8]-NRT-code), using
- OOA 3-folding [i] based on linear OA(6425, large, F64, 7) (dual of [large, large−25, 8]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16777217 | 648−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- OOA 3-folding [i] based on linear OA(6425, large, F64, 7) (dual of [large, large−25, 8]-code), using
- trace code [i] based on linear OOA(6425, 2796201, F64, 3, 7) (dual of [(2796201, 3), 8388578, 8]-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(862, large, F8, 3, 6) | [i] | Strength Reduction for OOAs | |
| 2 | Linear OOA(862, large, F8, 3, 5) | [i] | ||
| 3 | Linear OOA(862, large, F8, 3, 4) | [i] | ||
| 4 | Linear OOA(862, large, F8, 3, 3) | [i] | ||
| 5 | Linear OOA(865, large, F8, 3, 7) | [i] | NRT-Code Embedding in Larger Space | |
| 6 | Linear OOA(868, large, F8, 3, 7) | [i] | ||
| 7 | Linear OOA(871, large, F8, 3, 7) | [i] | ||
| 8 | Linear OOA(874, large, F8, 3, 7) | [i] | ||
| 9 | Linear OOA(877, large, F8, 3, 7) | [i] | ||
| 10 | Linear OOA(880, large, F8, 3, 7) | [i] | ||
| 11 | Linear OOA(886, large, F8, 3, 7) | [i] | ||
| 12 | Linear OOA(889, large, F8, 3, 7) | [i] | ||
| 13 | Linear OOA(892, large, F8, 3, 7) | [i] | ||
| 14 | Linear OOA(895, large, F8, 3, 7) | [i] | ||
| 15 | Linear OOA(898, large, F8, 3, 7) | [i] | ||
| 16 | Linear OOA(8101, large, F8, 3, 7) | [i] | ||
| 17 | Linear OOA(8104, large, F8, 3, 7) | [i] | ||
| 18 | Linear OOA(8110, large, F8, 3, 7) | [i] | ||
| 19 | Linear OOA(8113, large, F8, 3, 7) | [i] | ||
| 20 | Linear OOA(8116, large, F8, 3, 7) | [i] | ||
| 21 | Linear OOA(8119, large, F8, 3, 7) | [i] | ||
| 22 | Linear OOA(8122, large, F8, 3, 7) | [i] | ||
| 23 | Linear OOA(8125, large, F8, 3, 7) | [i] | ||
| 24 | Linear OOA(8128, large, F8, 3, 7) | [i] | ||
| 25 | Linear OOA(8134, large, F8, 3, 7) | [i] | ||
| 26 | Linear OOA(8137, large, F8, 3, 7) | [i] | ||
| 27 | Linear OOA(8140, large, F8, 3, 7) | [i] | ||
| 28 | Linear OOA(8143, large, F8, 3, 7) | [i] | ||
| 29 | Linear OOA(8146, large, F8, 3, 7) | [i] | ||
| 30 | Linear OOA(8149, large, F8, 3, 7) | [i] | ||
| 31 | Linear OOA(8152, large, F8, 3, 7) | [i] | ||
| 32 | Linear OOA(8158, large, F8, 3, 7) | [i] | ||
| 33 | Linear OOA(8161, large, F8, 3, 7) | [i] | ||
| 34 | Linear OOA(8164, large, F8, 3, 7) | [i] | ||
| 35 | Linear OOA(8167, large, F8, 3, 7) | [i] | ||
| 36 | Linear OOA(8170, large, F8, 3, 7) | [i] | ||
| 37 | Linear OOA(8173, large, F8, 3, 7) | [i] | ||
| 38 | Linear OOA(863, large, F8, 3, 7) | [i] | OOA Duplication | |
| 39 | Linear OOA(864, large, F8, 3, 7) | [i] | ||
| 40 | Linear OOA(862, 8388602, F8, 9, 7) (dual of [(8388602, 9), 75497356, 8]-NRT-code) | [i] | OOA Stacking with Additional Row | |