Information on Result #823842
Linear OOA(4190, 2097186, F4, 2, 22) (dual of [(2097186, 2), 4194182, 23]-NRT-code), using OOA 2-folding based on linear OA(4190, 4194372, F4, 22) (dual of [4194372, 4194182, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(14) [i] based on
- linear OA(4177, 4194304, F4, 22) (dual of [4194304, 4194127, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(4122, 4194304, F4, 15) (dual of [4194304, 4194182, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(413, 68, F4, 6) (dual of [68, 55, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(413, 70, F4, 6) (dual of [70, 57, 7]-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 OOA(4192, 2097187, F4, 2, 22) (dual of [(2097187, 2), 4194182, 23]-NRT-code) | [i] | NRT-Code Embedding in Larger Space | |
| 2 | Linear OOA(4191, 2097186, F4, 2, 22) (dual of [(2097186, 2), 4194181, 23]-NRT-code) | [i] | OOA Duplication | |
| 3 | Linear OOA(4190, 2097186, F4, 3, 22) (dual of [(2097186, 3), 6291368, 23]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Digital (168, 190, 2097186)-net over F4 | [i] | ||