Information on Result #2272820
Linear OA(4164, 16400, F4, 31) (dual of [16400, 16236, 32]-code), using 1 times code embedding in larger space based on linear OA(4163, 16399, F4, 31) (dual of [16399, 16236, 32]-code), using
- construction X applied to Ce(30) ⊂ Ce(28) [i] based on
- linear OA(4162, 16384, F4, 31) (dual of [16384, 16222, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(4148, 16384, F4, 29) (dual of [16384, 16236, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(41, 15, F4, 1) (dual of [15, 14, 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
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(4164, 9396, F4, 2, 31) (dual of [(9396, 2), 18628, 32]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4164, 9396, F4, 3, 31) (dual of [(9396, 3), 28024, 32]-NRT-code) | [i] | ||
| 3 | Digital (133, 164, 9396)-net over F4 | [i] | ||
| 4 | Linear OOA(4164, 8200, F4, 2, 31) (dual of [(8200, 2), 16236, 32]-NRT-code) | [i] | OOA Folding | |