Information on Result #682673
Linear OA(568, 15638, F5, 14) (dual of [15638, 15570, 15]-code), using construction X applied to Ce(13) ⊂ Ce(11) based on
- linear OA(567, 15625, F5, 14) (dual of [15625, 15558, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(555, 15625, F5, 12) (dual of [15625, 15570, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [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(568, 10557, F5, 2, 14) (dual of [(10557, 2), 21046, 15]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(568, 10557, F5, 3, 14) (dual of [(10557, 3), 31603, 15]-NRT-code) | [i] | ||
| 3 | Digital (54, 68, 10557)-net over F5 | [i] | ||
| 4 | Linear OOA(568, 7819, F5, 2, 14) (dual of [(7819, 2), 15570, 15]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(568, 5212, F5, 3, 14) (dual of [(5212, 3), 15568, 15]-NRT-code) | [i] | ||
| 6 | Linear OOA(568, 2234, F5, 14, 14) (dual of [(2234, 14), 31208, 15]-NRT-code) | [i] | OA Folding and Stacking | |