Information on Result #682665
Linear OA(5116, 15638, F5, 24) (dual of [15638, 15522, 25]-code), using construction X applied to Ce(23) ⊂ Ce(21) based on
- linear OA(5115, 15625, F5, 24) (dual of [15625, 15510, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(5103, 15625, F5, 22) (dual of [15625, 15522, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(51, 13, F5, 1) (dual of [13, 12, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(51, s, F5, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n 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, 10182, F5, 2, 24) (dual of [(10182, 2), 20248, 25]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(5116, 10182, F5, 3, 24) (dual of [(10182, 3), 30430, 25]-NRT-code) | [i] | ||
| 3 | Digital (92, 116, 10182)-net over F5 | [i] | ||
| 4 | Linear OOA(5116, 7819, F5, 2, 24) (dual of [(7819, 2), 15522, 25]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(5116, 5212, F5, 3, 24) (dual of [(5212, 3), 15520, 25]-NRT-code) | [i] | ||
| 6 | Linear OOA(5116, 1303, F5, 24, 24) (dual of [(1303, 24), 31156, 25]-NRT-code) | [i] | OA Folding and Stacking | |