Information on Result #962044
Linear OOA(4167, 1398105, F4, 3, 21) (dual of [(1398105, 3), 4194148, 22]-NRT-code), using OOA 3-folding based on linear OA(4167, 4194315, F4, 21) (dual of [4194315, 4194148, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(4167, 4194316, F4, 21) (dual of [4194316, 4194149, 22]-code), using
- construction X applied to Ce(20) ⊂ Ce(18) [i] based on
- 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(4155, 4194304, F4, 19) (dual of [4194304, 4194149, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(41, 12, F4, 1) (dual of [12, 11, 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(20) ⊂ Ce(18) [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 | Linear OOA(4168, 1398105, F4, 3, 21) (dual of [(1398105, 3), 4194147, 22]-NRT-code) | [i] | OOA Duplication | |
| 2 | Digital (146, 167, 1398105)-net over F4 | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |