Information on Result #824558
Linear OOA(4172, 32778, F4, 2, 28) (dual of [(32778, 2), 65384, 29]-NRT-code), using OOA 2-folding based on linear OA(4172, 65556, F4, 28) (dual of [65556, 65384, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(4172, 65557, F4, 28) (dual of [65557, 65385, 29]-code), using
- construction X applied to Ce(28) ⊂ Ce(24) [i] based on
- linear OA(4169, 65536, F4, 29) (dual of [65536, 65367, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(4145, 65536, F4, 25) (dual of [65536, 65391, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(43, 21, F4, 2) (dual of [21, 18, 3]-code), using
- Hamming code H(3,4) [i]
- construction X applied to Ce(28) ⊂ Ce(24) [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(4172, 32778, F4, 3, 28) (dual of [(32778, 3), 98162, 29]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (144, 172, 32778)-net over F4 | [i] | ||