Information on Result #962533
Linear OOA(4215, 1398114, F4, 3, 26) (dual of [(1398114, 3), 4194127, 27]-NRT-code), using OOA 3-folding based on linear OA(4215, 4194342, F4, 26) (dual of [4194342, 4194127, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(21) [i] based on
- linear OA(4210, 4194304, F4, 26) (dual of [4194304, 4194094, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- 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(45, 38, F4, 3) (dual of [38, 33, 4]-code or 38-cap in PG(4,4)), using
- discarding factors / shortening the dual code based on linear OA(45, 41, F4, 3) (dual of [41, 36, 4]-code or 41-cap in PG(4,4)), 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(4216, 1398114, F4, 3, 26) (dual of [(1398114, 3), 4194126, 27]-NRT-code) | [i] | OOA Duplication | |
| 2 | Digital (189, 215, 1398114)-net over F4 | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |