Information on Result #679156
Linear OA(4211, 16419, F4, 39) (dual of [16419, 16208, 40]-code), using construction X applied to Ce(38) ⊂ Ce(33) 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(4176, 16384, F4, 34) (dual of [16384, 16208, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(47, 35, F4, 4) (dual of [35, 28, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(47, 43, F4, 4) (dual of [43, 36, 5]-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 OA(4212, 16420, F4, 39) (dual of [16420, 16208, 40]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(4213, 16421, F4, 39) (dual of [16421, 16208, 40]-code) | [i] | ||
| 3 | Linear OOA(4211, 12731, F4, 2, 39) (dual of [(12731, 2), 25251, 40]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(4211, 12731, F4, 3, 39) (dual of [(12731, 3), 37982, 40]-NRT-code) | [i] | ||
| 5 | Digital (172, 211, 12731)-net over F4 | [i] | ||
| 6 | Linear OOA(4211, 8209, F4, 2, 39) (dual of [(8209, 2), 16207, 40]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(4211, 5473, F4, 3, 39) (dual of [(5473, 3), 16208, 40]-NRT-code) | [i] | ||