Information on Result #682680
Linear OA(538, 15638, F5, 8) (dual of [15638, 15600, 9]-code), using construction X applied to Ce(7) ⊂ Ce(5) based on
- linear OA(537, 15625, F5, 8) (dual of [15625, 15588, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(525, 15625, F5, 6) (dual of [15625, 15600, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [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(538, 15289, F5, 2, 8) (dual of [(15289, 2), 30540, 9]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(538, 15289, F5, 3, 8) (dual of [(15289, 3), 45829, 9]-NRT-code) | [i] | ||
| 3 | Digital (30, 38, 15289)-net over F5 | [i] | ||
| 4 | Linear OOA(538, 7819, F5, 2, 8) (dual of [(7819, 2), 15600, 9]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(538, 3909, F5, 8, 8) (dual of [(3909, 8), 31234, 9]-NRT-code) | [i] | OA Folding and Stacking | |