Information on Result #679714
Linear OA(4112, 4117, F4, 24) (dual of [4117, 4005, 25]-code), using construction X applied to Ce(24) ⊂ Ce(20) based on
- linear OA(4109, 4096, F4, 25) (dual of [4096, 3987, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(491, 4096, F4, 21) (dual of [4096, 4005, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [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(4112, 3274, F4, 2, 24) (dual of [(3274, 2), 6436, 25]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4112, 3274, F4, 3, 24) (dual of [(3274, 3), 9710, 25]-NRT-code) | [i] | ||
| 3 | Digital (88, 112, 3274)-net over F4 | [i] | ||
| 4 | Linear OA(4114, 4120, F4, 24) (dual of [4120, 4006, 25]-code) | [i] | Construction X with Varšamov Bound | |
| 5 | Linear OA(4115, 4122, F4, 24) (dual of [4122, 4007, 25]-code) | [i] | ||
| 6 | Linear OOA(4112, 2058, F4, 2, 24) (dual of [(2058, 2), 4004, 25]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(4112, 1372, F4, 3, 24) (dual of [(1372, 3), 4004, 25]-NRT-code) | [i] | ||