Information on Result #2688575
Linear OOA(4244, 1398105, F4, 3, 30) (dual of [(1398105, 3), 4194071, 31]-NRT-code), using 41 times duplication based on linear OOA(4243, 1398105, F4, 3, 30) (dual of [(1398105, 3), 4194072, 31]-NRT-code), using
- OOA 3-folding [i] based on linear OA(4243, 4194315, F4, 30) (dual of [4194315, 4194072, 31]-code), using
- construction X applied to Ce(29) ⊂ Ce(28) [i] based on
- linear OA(4243, 4194304, F4, 30) (dual of [4194304, 4194061, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- 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(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
- construction X applied to Ce(29) ⊂ Ce(28) [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 (214, 244, 1339054)-net over F4 | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |