Information on Result #2496846
Linear OOA(4254, 2097179, F4, 2, 30) (dual of [(2097179, 2), 4194104, 31]-NRT-code), using 41 times duplication based on linear OOA(4253, 2097179, F4, 2, 30) (dual of [(2097179, 2), 4194105, 31]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(4251, 2097178, F4, 2, 30) (dual of [(2097178, 2), 4194105, 31]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4251, 4194356, F4, 30) (dual of [4194356, 4194105, 31]-code), using
- construction X applied to Ce(29) ⊂ Ce(24) [i] based on
- linear OA(4243, 4194304, F4, 30) (dual of [4194304, 4194061, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(4199, 4194304, F4, 25) (dual of [4194304, 4194105, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(48, 52, F4, 4) (dual of [52, 44, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(48, 85, F4, 4) (dual of [85, 77, 5]-code), using
- construction X applied to Ce(29) ⊂ Ce(24) [i] based on
- OOA 2-folding [i] based on linear OA(4251, 4194356, F4, 30) (dual of [4194356, 4194105, 31]-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(4254, 1515326, F4, 3, 30) (dual of [(1515326, 3), 4545724, 31]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (224, 254, 1515326)-net over F4 | [i] | ||