Information on Result #962131
Linear OOA(4177, 1398105, F4, 3, 22) (dual of [(1398105, 3), 4194138, 23]-NRT-code), using OOA 3-folding based on linear OA(4177, 4194315, F4, 22) (dual of [4194315, 4194138, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(20) [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(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(40, 11, F4, 0) (dual of [11, 11, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(40, s, F4, 0) (dual of [s, s, 1]-code) for arbitrarily large s, 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(4178, 1398105, F4, 3, 22) (dual of [(1398105, 3), 4194137, 23]-NRT-code) | [i] | OOA Duplication | |
| 2 | Linear OOA(4179, 1398105, F4, 3, 22) (dual of [(1398105, 3), 4194136, 23]-NRT-code) | [i] | ||
| 3 | Digital (155, 177, 1398105)-net over F4 | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |