Information on Result #679688
Linear OA(4192, 4119, F4, 42) (dual of [4119, 3927, 43]-code), using construction X applied to Ce(41) ⊂ Ce(37) based on
- linear OA(4187, 4096, F4, 42) (dual of [4096, 3909, 43]-code), using an extension Ce(41) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,41], and designed minimum distance d ≥ |I|+1 = 42 [i]
- linear OA(4169, 4096, F4, 38) (dual of [4096, 3927, 39]-code), using an extension Ce(37) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,37], and designed minimum distance d ≥ |I|+1 = 38 [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(4192, 3909, F4, 2, 42) (dual of [(3909, 2), 7626, 43]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4192, 3909, F4, 3, 42) (dual of [(3909, 3), 11535, 43]-NRT-code) | [i] | ||
| 3 | Digital (150, 192, 3909)-net over F4 | [i] | ||
| 4 | Linear OOA(4192, 2059, F4, 2, 42) (dual of [(2059, 2), 3926, 43]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(4192, 1373, F4, 3, 42) (dual of [(1373, 3), 3927, 43]-NRT-code) | [i] | ||