Information on Result #679756
Linear OA(4158, 4127, F4, 34) (dual of [4127, 3969, 35]-code), using construction X applied to Ce(33) ⊂ Ce(28) based on
- linear OA(4151, 4096, F4, 34) (dual of [4096, 3945, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(4127, 4096, F4, 29) (dual of [4096, 3969, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(47, 31, F4, 4) (dual of [31, 24, 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(4159, 4128, F4, 34) (dual of [4128, 3969, 35]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(4158, 3809, F4, 2, 34) (dual of [(3809, 2), 7460, 35]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(4158, 3809, F4, 3, 34) (dual of [(3809, 3), 11269, 35]-NRT-code) | [i] | ||
| 4 | Digital (124, 158, 3809)-net over F4 | [i] | ||
| 5 | Linear OA(4161, 4132, F4, 34) (dual of [4132, 3971, 35]-code) | [i] | Construction X with Varšamov Bound | |
| 6 | Linear OA(4162, 4134, F4, 34) (dual of [4134, 3972, 35]-code) | [i] | ||
| 7 | Linear OOA(4158, 2063, F4, 2, 34) (dual of [(2063, 2), 3968, 35]-NRT-code) | [i] | OOA Folding | |
| 8 | Linear OOA(4158, 1375, F4, 3, 34) (dual of [(1375, 3), 3967, 35]-NRT-code) | [i] | ||