Information on Result #824744
Linear OOA(4250, 2097194, F4, 2, 29) (dual of [(2097194, 2), 4194138, 30]-NRT-code), using OOA 2-folding based on linear OA(4250, 4194388, F4, 29) (dual of [4194388, 4194138, 30]-code), using
- construction X applied to Ce(28) ⊂ Ce(20) [i] based on
- 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(4166, 4194304, F4, 21) (dual of [4194304, 4194138, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(418, 84, F4, 7) (dual of [84, 66, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(418, 85, F4, 7) (dual of [85, 67, 8]-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(4250, 2097194, F4, 2, 28) (dual of [(2097194, 2), 4194138, 29]-NRT-code) | [i] | Strength Reduction for OOAs | |
| 2 | Linear OOA(4252, 2097195, F4, 2, 29) (dual of [(2097195, 2), 4194138, 30]-NRT-code) | [i] | NRT-Code Embedding in Larger Space | |
| 3 | Linear OOA(4251, 2097194, F4, 2, 29) (dual of [(2097194, 2), 4194137, 30]-NRT-code) | [i] | OOA Duplication | |
| 4 | Linear OOA(4249, 2097193, F4, 2, 28) (dual of [(2097193, 2), 4194137, 29]-NRT-code) | [i] | Truncation for OOAs | |
| 5 | Linear OOA(4250, 1944882, F4, 3, 29) (dual of [(1944882, 3), 5834396, 30]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 6 | Digital (221, 250, 1944882)-net over F4 | [i] | ||