Information on Result #682507
Linear OA(562, 78158, F5, 10) (dual of [78158, 78096, 11]-code), using construction X applied to Ce(10) ⊂ Ce(5) based on
- linear OA(557, 78125, F5, 11) (dual of [78125, 78068, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(529, 78125, F5, 6) (dual of [78125, 78096, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(55, 33, F5, 3) (dual of [33, 28, 4]-code or 33-cap in PG(4,5)), using
- discarding factors / shortening the dual code based on linear OA(55, 42, F5, 3) (dual of [42, 37, 4]-code or 42-cap in PG(4,5)), 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(562, 78158, F5, 2, 10) (dual of [(78158, 2), 156254, 11]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(562, 78158, F5, 3, 10) (dual of [(78158, 3), 234412, 11]-NRT-code) | [i] | ||
| 3 | Digital (52, 62, 78158)-net over F5 | [i] | ||
| 4 | Linear OOA(562, 39079, F5, 2, 10) (dual of [(39079, 2), 78096, 11]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(562, 26052, F5, 3, 10) (dual of [(26052, 3), 78094, 11]-NRT-code) | [i] | ||
| 6 | Linear OOA(562, 15631, F5, 10, 10) (dual of [(15631, 10), 156248, 11]-NRT-code) | [i] | OA Folding and Stacking | |