Information on Result #682677
Linear OA(550, 15639, F5, 10) (dual of [15639, 15589, 11]-code), using construction X4 applied to Ce(10) ⊂ Ce(7) based on
- linear OA(549, 15625, F5, 11) (dual of [15625, 15576, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- 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(513, 14, F5, 13) (dual of [14, 1, 14]-code or 14-arc in PG(12,5)), using
- dual of repetition code with length 14 [i]
- linear OA(51, 14, F5, 1) (dual of [14, 13, 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 OA(551, 15640, F5, 10) (dual of [15640, 15589, 11]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(550, 15639, F5, 2, 10) (dual of [(15639, 2), 31228, 11]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(550, 15639, F5, 3, 10) (dual of [(15639, 3), 46867, 11]-NRT-code) | [i] | ||
| 4 | Digital (40, 50, 15639)-net over F5 | [i] | ||
| 5 | Linear OA(551, 15641, F5, 10) (dual of [15641, 15590, 11]-code) | [i] | Construction X with Varšamov Bound | |
| 6 | Linear OOA(550, 5213, F5, 3, 10) (dual of [(5213, 3), 15589, 11]-NRT-code) | [i] | OOA Folding | |