Information on Result #679155
Linear OA(4225, 16419, F4, 42) (dual of [16419, 16194, 43]-code), using construction X applied to Ce(41) ⊂ Ce(36) based on
- linear OA(4218, 16384, F4, 42) (dual of [16384, 16166, 43]-code), using an extension Ce(41) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,41], and designed minimum distance d ≥ |I|+1 = 42 [i]
- linear OA(4190, 16384, F4, 37) (dual of [16384, 16194, 38]-code), using an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [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(4226, 16420, F4, 42) (dual of [16420, 16194, 43]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(4227, 16421, F4, 42) (dual of [16421, 16194, 43]-code) | [i] | ||
| 3 | Linear OA(4228, 16422, F4, 42) (dual of [16422, 16194, 43]-code) | [i] | ||
| 4 | Linear OA(4229, 16423, F4, 42) (dual of [16423, 16194, 43]-code) | [i] | ||
| 5 | Linear OA(4230, 16424, F4, 42) (dual of [16424, 16194, 43]-code) | [i] | ||
| 6 | Linear OOA(4225, 12333, F4, 2, 42) (dual of [(12333, 2), 24441, 43]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 7 | Linear OOA(4225, 12333, F4, 3, 42) (dual of [(12333, 3), 36774, 43]-NRT-code) | [i] | ||
| 8 | Digital (183, 225, 12333)-net over F4 | [i] | ||
| 9 | Linear OA(4228, 16423, F4, 42) (dual of [16423, 16195, 43]-code) | [i] | Construction X with Varšamov Bound | |
| 10 | Linear OA(4229, 16425, F4, 42) (dual of [16425, 16196, 43]-code) | [i] | ||
| 11 | Linear OA(4230, 16427, F4, 42) (dual of [16427, 16197, 43]-code) | [i] | ||
| 12 | Linear OOA(4225, 8209, F4, 2, 42) (dual of [(8209, 2), 16193, 43]-NRT-code) | [i] | OOA Folding | |
| 13 | Linear OOA(4225, 5473, F4, 3, 42) (dual of [(5473, 3), 16194, 43]-NRT-code) | [i] | ||