Information on Result #962752
Linear OOA(4232, 1398105, F4, 3, 28) (dual of [(1398105, 3), 4194083, 29]-NRT-code), using OOA 3-folding based on linear OA(4232, 4194315, F4, 28) (dual of [4194315, 4194083, 29]-code), using
- 1 times truncation [i] based on linear OA(4233, 4194316, F4, 29) (dual of [4194316, 4194083, 30]-code), using
- construction X applied to Ce(28) ⊂ Ce(26) [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(4221, 4194304, F4, 27) (dual of [4194304, 4194083, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [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(28) ⊂ Ce(26) [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 | Digital (204, 232, 1398105)-net over F4 | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |