Information on Result #824999
Linear OOA(4189, 32779, F4, 2, 31) (dual of [(32779, 2), 65369, 32]-NRT-code), using OOA 2-folding based on linear OA(4189, 65558, F4, 31) (dual of [65558, 65369, 32]-code), using
- construction XX applied to Ce(30) ⊂ Ce(28) ⊂ Ce(26) [i] based on
- linear OA(4185, 65536, F4, 31) (dual of [65536, 65351, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- 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(4161, 65536, F4, 27) (dual of [65536, 65375, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(41, 19, F4, 1) (dual of [19, 18, 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
- linear OA(41, 3, F4, 1) (dual of [3, 2, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(41, 4, F4, 1) (dual of [4, 3, 2]-code), using
- Reed–Solomon code RS(3,4) [i]
- discarding factors / shortening the dual code based on linear OA(41, 4, F4, 1) (dual of [4, 3, 2]-code), 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(4189, 32779, F4, 3, 31) (dual of [(32779, 3), 98148, 32]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (158, 189, 32779)-net over F4 | [i] | ||