Information on Result #1013045
Linear OOA(5113, 8388602, F5, 3, 9) (dual of [(8388602, 3), 25165693, 10]-NRT-code), using (u, u+v)-construction 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
- linear OOA(582, 4194301, F5, 3, 9) (dual of [(4194301, 3), 12582821, 10]-NRT-code), using
- OOA 2-folding [i] based on linear OOA(582, 8388602, F5, 2, 9) (dual of [(8388602, 2), 16777122, 10]-NRT-code), using
- trace code [i] based on linear OOA(2541, 4194301, F25, 2, 9) (dual of [(4194301, 2), 8388561, 10]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2541, 8388602, F25, 9) (dual of [8388602, 8388561, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(2541, large, F25, 9) (dual of [large, large−41, 10]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 9765626 | 2510−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(2541, large, F25, 9) (dual of [large, large−41, 10]-code), using
- OOA 2-folding [i] based on linear OA(2541, 8388602, F25, 9) (dual of [8388602, 8388561, 10]-code), using
- trace code [i] based on linear OOA(2541, 4194301, F25, 2, 9) (dual of [(4194301, 2), 8388561, 10]-NRT-code), using
- OOA 2-folding [i] based on linear OOA(582, 8388602, F5, 2, 9) (dual of [(8388602, 2), 16777122, 10]-NRT-code), using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, k and s, k and t, m and s, 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(5116, large, F5, 3, 9) | [i] | NRT-Code Embedding in Larger Space | |
| 2 | Linear OOA(5119, large, F5, 3, 9) | [i] | ||
| 3 | Linear OOA(5122, large, F5, 3, 9) | [i] | ||
| 4 | Linear OOA(5125, large, F5, 3, 9) | [i] | ||
| 5 | Linear OOA(5128, large, F5, 3, 9) | [i] | ||
| 6 | Linear OOA(5131, large, F5, 3, 9) | [i] | ||
| 7 | Linear OOA(5134, large, F5, 3, 9) | [i] | ||
| 8 | Linear OOA(5137, large, F5, 3, 9) | [i] | ||
| 9 | Linear OOA(5143, large, F5, 3, 9) | [i] | ||
| 10 | Linear OOA(5146, large, F5, 3, 9) | [i] | ||
| 11 | Linear OOA(5149, large, F5, 3, 9) | [i] | ||
| 12 | Linear OOA(5114, 8388602, F5, 3, 9) (dual of [(8388602, 3), 25165692, 10]-NRT-code) | [i] | OOA Duplication | |
| 13 | Linear OOA(5115, 8388602, F5, 3, 9) (dual of [(8388602, 3), 25165691, 10]-NRT-code) | [i] | ||