Information on Result #737568
Linear OA(5142, 15664, F5, 28) (dual of [15664, 15522, 29]-code), using construction X applied to Ce(27) ⊂ Ce(21) based on
- linear OA(5133, 15625, F5, 28) (dual of [15625, 15492, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(5103, 15625, F5, 22) (dual of [15625, 15522, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(59, 39, F5, 5) (dual of [39, 30, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(59, 44, F5, 5) (dual of [44, 35, 6]-code), 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(5142, 15664, F5, 2, 28) (dual of [(15664, 2), 31186, 29]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(5142, 15664, F5, 3, 28) (dual of [(15664, 3), 46850, 29]-NRT-code) | [i] | ||
| 3 | Digital (114, 142, 15664)-net over F5 | [i] | ||
| 4 | Linear OA(5143, 15666, F5, 28) (dual of [15666, 15523, 29]-code) | [i] | Construction X with Varšamov Bound | |
| 5 | Linear OOA(5142, 7832, F5, 2, 28) (dual of [(7832, 2), 15522, 29]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(5142, 5221, F5, 3, 28) (dual of [(5221, 3), 15521, 29]-NRT-code) | [i] | ||