Information on Result #2694330
Linear OOA(5109, large, F5, 3, 4), using 25 times NRT-code embedding in larger space based on linear OOA(534, large, F5, 3, 4), using
- (u, u+v)-construction [i] based on
- linear OOA(52, 6, F5, 3, 2) (dual of [(6, 3), 16, 3]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(3;16,5) [i]
- linear OOA(532, 8388601, F5, 3, 4) (dual of [(8388601, 3), 25165771, 5]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(532, 8388602, F5, 2, 4) (dual of [(8388602, 2), 16777172, 5]-NRT-code), using
- trace code [i] based on linear OOA(2516, 4194301, F25, 2, 4) (dual of [(4194301, 2), 8388586, 5]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2516, 8388602, F25, 4) (dual of [8388602, 8388586, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(2516, large, F25, 4) (dual of [large, large−16, 5]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 9765624 = 255−1, defining interval I = [0,3], and designed minimum distance d ≥ |I|+1 = 5 [i]
- discarding factors / shortening the dual code based on linear OA(2516, large, F25, 4) (dual of [large, large−16, 5]-code), using
- OOA 2-folding [i] based on linear OA(2516, 8388602, F25, 4) (dual of [8388602, 8388586, 5]-code), using
- trace code [i] based on linear OOA(2516, 4194301, F25, 2, 4) (dual of [(4194301, 2), 8388586, 5]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(532, 8388602, F5, 2, 4) (dual of [(8388602, 2), 16777172, 5]-NRT-code), using
- linear OOA(52, 6, F5, 3, 2) (dual of [(6, 3), 16, 3]-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(5110, large, F5, 3, 4) | [i] | OOA Duplication | |
| 2 | Linear OOA(5111, large, F5, 3, 4) | [i] | ||