Information on Result #679690
Linear OA(4184, 4117, F4, 40) (dual of [4117, 3933, 41]-code), using construction X applied to Ce(40) ⊂ Ce(36) based on
- linear OA(4181, 4096, F4, 41) (dual of [4096, 3915, 42]-code), using an extension Ce(40) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,40], and designed minimum distance d ≥ |I|+1 = 41 [i]
- linear OA(4163, 4096, F4, 37) (dual of [4096, 3933, 38]-code), using an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(43, 21, F4, 2) (dual of [21, 18, 3]-code), using
- Hamming code H(3,4) [i]
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(4184, 3943, F4, 2, 40) (dual of [(3943, 2), 7702, 41]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4184, 3943, F4, 3, 40) (dual of [(3943, 3), 11645, 41]-NRT-code) | [i] | ||
| 3 | Digital (144, 184, 3943)-net over F4 | [i] | ||
| 4 | Linear OA(4185, 4119, F4, 40) (dual of [4119, 3934, 41]-code) | [i] | Construction X with Varšamov Bound | |
| 5 | Linear OA(4186, 4121, F4, 40) (dual of [4121, 3935, 41]-code) | [i] | ||
| 6 | Linear OA(4187, 4123, F4, 40) (dual of [4123, 3936, 41]-code) | [i] | ||
| 7 | Linear OOA(4184, 2058, F4, 2, 40) (dual of [(2058, 2), 3932, 41]-NRT-code) | [i] | OOA Folding | |
| 8 | Linear OOA(4184, 1372, F4, 3, 40) (dual of [(1372, 3), 3932, 41]-NRT-code) | [i] | ||