Information on Result #2797809
Linear OOA(3242, large, F3, 4, 13), using 10 times NRT-code embedding in larger space based on linear OOA(3202, large, F3, 4, 13), using
- (u, u+v)-construction [i] based on
- linear OOA(36, 4, F3, 4, 6) (dual of [(4, 4), 10, 7]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(4;10,3) [i]
- linear OOA(3196, 8388600, F3, 4, 13) (dual of [(8388600, 4), 33554204, 14]-NRT-code), using
- trace code [i] based on linear OOA(8149, 2097150, F81, 4, 13) (dual of [(2097150, 4), 8388551, 14]-NRT-code), using
- OOA 4-folding [i] based on linear OA(8149, 8388600, F81, 13) (dual of [8388600, 8388551, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(8149, large, F81, 13) (dual of [large, large−49, 14]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523361 | 818−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(8149, large, F81, 13) (dual of [large, large−49, 14]-code), using
- OOA 4-folding [i] based on linear OA(8149, 8388600, F81, 13) (dual of [8388600, 8388551, 14]-code), using
- trace code [i] based on linear OOA(8149, 2097150, F81, 4, 13) (dual of [(2097150, 4), 8388551, 14]-NRT-code), using
- linear OOA(36, 4, F3, 4, 6) (dual of [(4, 4), 10, 7]-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(3243, large, F3, 4, 13) | [i] | OOA Duplication | |
| 2 | Linear OOA(3244, large, F3, 4, 13) | [i] | ||
| 3 | Linear OOA(3245, large, F3, 4, 13) | [i] | ||