Information on Result #823591
Linear OOA(4124, 32778, F4, 2, 20) (dual of [(32778, 2), 65432, 21]-NRT-code), using OOA 2-folding based on linear OA(4124, 65556, F4, 20) (dual of [65556, 65432, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(4124, 65557, F4, 20) (dual of [65557, 65433, 21]-code), using
- construction X applied to Ce(20) ⊂ Ce(16) [i] based on
- linear OA(4121, 65536, F4, 21) (dual of [65536, 65415, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(497, 65536, F4, 17) (dual of [65536, 65439, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [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(20) ⊂ Ce(16) [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(4124, 32778, F4, 3, 20) (dual of [(32778, 3), 98210, 21]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (104, 124, 32778)-net over F4 | [i] | ||