Information on Result #679163
Linear OA(4162, 16419, F4, 30) (dual of [16419, 16257, 31]-code), using construction X applied to Ce(29) ⊂ Ce(24) based on
- linear OA(4155, 16384, F4, 30) (dual of [16384, 16229, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(4127, 16384, F4, 25) (dual of [16384, 16257, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(47, 35, F4, 4) (dual of [35, 28, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(47, 43, F4, 4) (dual of [43, 36, 5]-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 OA(4163, 16420, F4, 30) (dual of [16420, 16257, 31]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(4164, 16421, F4, 30) (dual of [16421, 16257, 31]-code) | [i] | ||
| 3 | Linear OA(4165, 16422, F4, 30) (dual of [16422, 16257, 31]-code) | [i] | ||
| 4 | Linear OA(4166, 16423, F4, 30) (dual of [16423, 16257, 31]-code) | [i] | ||
| 5 | Linear OA(4167, 16424, F4, 30) (dual of [16424, 16257, 31]-code) | [i] | ||
| 6 | Linear OOA(4162, 10885, F4, 2, 30) (dual of [(10885, 2), 21608, 31]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 7 | Linear OOA(4162, 10885, F4, 3, 30) (dual of [(10885, 3), 32493, 31]-NRT-code) | [i] | ||
| 8 | Digital (132, 162, 10885)-net over F4 | [i] | ||
| 9 | Linear OA(4165, 16423, F4, 30) (dual of [16423, 16258, 31]-code) | [i] | Construction X with Varšamov Bound | |
| 10 | Linear OA(4166, 16425, F4, 30) (dual of [16425, 16259, 31]-code) | [i] | ||
| 11 | Linear OA(4167, 16427, F4, 30) (dual of [16427, 16260, 31]-code) | [i] | ||
| 12 | Linear OOA(4162, 8209, F4, 2, 30) (dual of [(8209, 2), 16256, 31]-NRT-code) | [i] | OOA Folding | |
| 13 | Linear OOA(4162, 5473, F4, 3, 30) (dual of [(5473, 3), 16257, 31]-NRT-code) | [i] | ||