Information on Result #1323791
Linear OA(5133, 78180, F5, 22) (dual of [78180, 78047, 23]-code), using construction X applied to Ce(21) ⊂ Ce(13) based on
- linear OA(5120, 78125, F5, 22) (dual of [78125, 78005, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(578, 78125, F5, 14) (dual of [78125, 78047, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(513, 55, F5, 7) (dual of [55, 42, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(513, 63, F5, 7) (dual of [63, 50, 8]-code), using
- a “GraCyc†code from Grassl’s database [i]
- discarding factors / shortening the dual code based on linear OA(513, 63, F5, 7) (dual of [63, 50, 8]-code), using
Mode: 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(5133, 78180, F5, 2, 22) (dual of [(78180, 2), 156227, 23]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(5133, 78180, F5, 3, 22) (dual of [(78180, 3), 234407, 23]-NRT-code) | [i] | ||
| 3 | Digital (111, 133, 78180)-net over F5 | [i] | ||
| 4 | Linear OA(5134, 78182, F5, 22) (dual of [78182, 78048, 23]-code) | [i] | Construction X with Varšamov Bound | |
| 5 | Linear OA(5135, 78184, F5, 22) (dual of [78184, 78049, 23]-code) | [i] | ||
| 6 | Linear OOA(5133, 39090, F5, 2, 22) (dual of [(39090, 2), 78047, 23]-NRT-code) | [i] | OOA Folding | |