Information on Result #2694682
Linear OOA(5133, large, F5, 3, 8), using 10 times NRT-code embedding in larger space based on linear OOA(5103, large, F5, 3, 8), using
- generalized (u, u+v)-construction [i] based on
- linear OOA(511, 2796201, F5, 3, 2) (dual of [(2796201, 3), 8388592, 3]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(511, large, F5, 3, 2), using
- appending 1 arbitrary column [i] based on linear OOA(511, large, F5, 2, 2), using
- appending kth column [i] based on linear OA(511, large, F5, 2) (dual of [large, large−11, 3]-code), using
- Hamming code H(11,5) [i]
- appending kth column [i] based on linear OA(511, large, F5, 2) (dual of [large, large−11, 3]-code), using
- appending 1 arbitrary column [i] based on linear OOA(511, large, F5, 2, 2), using
- discarding factors / shortening the dual code based on linear OOA(511, large, F5, 3, 2), using
- linear OOA(531, 2796201, F5, 3, 4) (dual of [(2796201, 3), 8388572, 5]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(531, 4194301, F5, 3, 4) (dual of [(4194301, 3), 12582872, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(531, 8388602, F5, 4) (dual of [8388602, 8388571, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(531, large, F5, 4) (dual of [large, large−31, 5]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 9765624 = 510−1, defining interval I = [0,3], and designed minimum distance d ≥ |I|+1 = 5 [i]
- discarding factors / shortening the dual code based on linear OA(531, large, F5, 4) (dual of [large, large−31, 5]-code), using
- OA 2-folding and stacking [i] based on linear OA(531, 8388602, F5, 4) (dual of [8388602, 8388571, 5]-code), using
- discarding factors / shortening the dual code based on linear OOA(531, 4194301, F5, 3, 4) (dual of [(4194301, 3), 12582872, 5]-NRT-code), using
- linear OOA(561, 2796201, F5, 3, 8) (dual of [(2796201, 3), 8388542, 9]-NRT-code), using
- OOA 3-folding [i] based on linear OA(561, large, F5, 8) (dual of [large, large−61, 9]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 9765624 = 510−1, defining interval I = [0,7], and designed minimum distance d ≥ |I|+1 = 9 [i]
- OOA 3-folding [i] based on linear OA(561, large, F5, 8) (dual of [large, large−61, 9]-code), using
- linear OOA(511, 2796201, F5, 3, 2) (dual of [(2796201, 3), 8388592, 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(5134, large, F5, 3, 8) | [i] | OOA Duplication | |
| 2 | Linear OOA(5135, large, F5, 3, 8) | [i] | ||