Information on Result #679698
Linear OA(4162, 4119, F4, 35) (dual of [4119, 3957, 36]-code), using construction X applied to Ce(34) ⊂ Ce(30) based on
- linear OA(4157, 4096, F4, 35) (dual of [4096, 3939, 36]-code), using an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(4139, 4096, F4, 31) (dual of [4096, 3957, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(45, 23, F4, 3) (dual of [23, 18, 4]-code or 23-cap in PG(4,4)), using
- discarding factors / shortening the dual code based on linear OA(45, 41, F4, 3) (dual of [41, 36, 4]-code or 41-cap in PG(4,4)), 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(4162, 3772, F4, 2, 35) (dual of [(3772, 2), 7382, 36]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4162, 3772, F4, 3, 35) (dual of [(3772, 3), 11154, 36]-NRT-code) | [i] | ||
| 3 | Digital (127, 162, 3772)-net over F4 | [i] | ||
| 4 | Linear OOA(4162, 2059, F4, 2, 35) (dual of [(2059, 2), 3956, 36]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(4162, 1373, F4, 3, 35) (dual of [(1373, 3), 3957, 36]-NRT-code) | [i] | ||