Information on Result #679073
Linear OA(4205, 16399, F4, 39) (dual of [16399, 16194, 40]-code), using construction X applied to Ce(38) ⊂ Ce(36) based on
- linear OA(4204, 16384, F4, 39) (dual of [16384, 16180, 40]-code), using an extension Ce(38) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,38], and designed minimum distance d ≥ |I|+1 = 39 [i]
- linear OA(4190, 16384, F4, 37) (dual of [16384, 16194, 38]-code), using an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [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 OA(4206, 16400, F4, 39) (dual of [16400, 16194, 40]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(4205, 10162, F4, 2, 39) (dual of [(10162, 2), 20119, 40]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(4205, 10162, F4, 3, 39) (dual of [(10162, 3), 30281, 40]-NRT-code) | [i] | ||
| 4 | Digital (166, 205, 10162)-net over F4 | [i] | ||
| 5 | Linear OOA(4205, 8199, F4, 2, 39) (dual of [(8199, 2), 16193, 40]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(4205, 5466, F4, 3, 39) (dual of [(5466, 3), 16193, 40]-NRT-code) | [i] | ||