Information on Result #2688690
Linear OOA(4258, 1398110, F4, 3, 31) (dual of [(1398110, 3), 4194072, 32]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(4255, 1398109, F4, 3, 31) (dual of [(1398109, 3), 4194072, 32]-NRT-code), using
- OOA 3-folding [i] based on linear OA(4255, 4194327, F4, 31) (dual of [4194327, 4194072, 32]-code), using
- construction X applied to Ce(30) ⊂ Ce(28) [i] based on
- linear OA(4254, 4194304, F4, 31) (dual of [4194304, 4194050, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(4232, 4194304, F4, 29) (dual of [4194304, 4194072, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(41, 23, F4, 1) (dual of [23, 22, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(41, s, F4, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to Ce(30) ⊂ Ce(28) [i] based on
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 | Digital (227, 258, 1398110)-net over F4 | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |