Information on Result #679162
Linear OA(4169, 16419, F4, 31) (dual of [16419, 16250, 32]-code), using construction X applied to Ce(30) ⊂ Ce(25) based on
- linear OA(4162, 16384, F4, 31) (dual of [16384, 16222, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(4134, 16384, F4, 26) (dual of [16384, 16250, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [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(4170, 16420, F4, 31) (dual of [16420, 16250, 32]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(4171, 16421, F4, 31) (dual of [16421, 16250, 32]-code) | [i] | ||
| 3 | Linear OOA(4169, 11939, F4, 2, 31) (dual of [(11939, 2), 23709, 32]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(4169, 11939, F4, 3, 31) (dual of [(11939, 3), 35648, 32]-NRT-code) | [i] | ||
| 5 | Digital (138, 169, 11939)-net over F4 | [i] | ||
| 6 | Linear OOA(4169, 8209, F4, 2, 31) (dual of [(8209, 2), 16249, 32]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(4169, 5473, F4, 3, 31) (dual of [(5473, 3), 16250, 32]-NRT-code) | [i] | ||