Information on Result #682452
Linear OA(5135, 78140, F5, 24) (dual of [78140, 78005, 25]-code), using construction X applied to Ce(23) ⊂ Ce(21) based on
- linear OA(5134, 78125, F5, 24) (dual of [78125, 77991, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- 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(51, 15, F5, 1) (dual of [15, 14, 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(5135, 40925, F5, 2, 24) (dual of [(40925, 2), 81715, 25]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(5135, 40925, F5, 3, 24) (dual of [(40925, 3), 122640, 25]-NRT-code) | [i] | ||
| 3 | Digital (111, 135, 40925)-net over F5 | [i] | ||
| 4 | Linear OOA(5135, 39070, F5, 2, 24) (dual of [(39070, 2), 78005, 25]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(5135, 26046, F5, 3, 24) (dual of [(26046, 3), 78003, 25]-NRT-code) | [i] | ||