Information on Result #1082917
Linear OOA(12857, large, F128, 4, 8), using (u, u+v)-construction based on
- linear OOA(12813, 4194301, F128, 4, 4) (dual of [(4194301, 4), 16777191, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(12813, 8388602, F128, 4) (dual of [8388602, 8388589, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(12813, large, F128, 4) (dual of [large, large−13, 5]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 17895697 | 1284−1, defining interval I = [0,3], and designed minimum distance d ≥ |I|+1 = 5 [i]
- discarding factors / shortening the dual code based on linear OA(12813, large, F128, 4) (dual of [large, large−13, 5]-code), using
- OA 2-folding and stacking [i] based on linear OA(12813, 8388602, F128, 4) (dual of [8388602, 8388589, 5]-code), using
- linear OOA(12844, 4194302, F128, 4, 8) (dual of [(4194302, 4), 16777164, 9]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(12813, 4194301, F128, 4, 4) (dual of [(4194301, 4), 16777191, 5]-NRT-code) (see above)
- linear OOA(12831, 2097151, F128, 4, 8) (dual of [(2097151, 4), 8388573, 9]-NRT-code), using
- OOA 2-folding [i] based on linear OOA(12831, 4194302, F128, 2, 8) (dual of [(4194302, 2), 8388573, 9]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(12829, 4194301, F128, 2, 8) (dual of [(4194301, 2), 8388573, 9]-NRT-code), using
- OOA 2-folding [i] based on linear OA(12829, 8388602, F128, 8) (dual of [8388602, 8388573, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(12829, large, F128, 8) (dual of [large, large−29, 9]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 17895697 | 1284−1, defining interval I = [0,7], and designed minimum distance d ≥ |I|+1 = 9 [i]
- discarding factors / shortening the dual code based on linear OA(12829, large, F128, 8) (dual of [large, large−29, 9]-code), using
- OOA 2-folding [i] based on linear OA(12829, 8388602, F128, 8) (dual of [8388602, 8388573, 9]-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(12829, 4194301, F128, 2, 8) (dual of [(4194301, 2), 8388573, 9]-NRT-code), using
- OOA 2-folding [i] based on linear OOA(12831, 4194302, F128, 2, 8) (dual of [(4194302, 2), 8388573, 9]-NRT-code), using
- (u, u+v)-construction [i] based on
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(12857, large, F128, 4, 7) | [i] | Strength Reduction for OOAs | |
| 2 | Linear OOA(12857, large, F128, 4, 6) | [i] | ||
| 3 | Linear OOA(12857, large, F128, 4, 5) | [i] | ||
| 4 | Linear OOA(12857, large, F128, 4, 4) | [i] | ||
| 5 | Linear OOA(12857, large, F128, 4, 3) | [i] | ||