Information on Result #679157
Linear OA(4204, 16419, F4, 38) (dual of [16419, 16215, 39]-code), using construction X applied to Ce(37) ⊂ Ce(32) based on
- linear OA(4197, 16384, F4, 38) (dual of [16384, 16187, 39]-code), using an extension Ce(37) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,37], and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(4169, 16384, F4, 33) (dual of [16384, 16215, 34]-code), using an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [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(4205, 16420, F4, 38) (dual of [16420, 16215, 39]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(4206, 16421, F4, 38) (dual of [16421, 16215, 39]-code) | [i] | ||
| 3 | Linear OA(4207, 16422, F4, 38) (dual of [16422, 16215, 39]-code) | [i] | ||
| 4 | Linear OA(4208, 16423, F4, 38) (dual of [16423, 16215, 39]-code) | [i] | ||
| 5 | Linear OA(4209, 16424, F4, 38) (dual of [16424, 16215, 39]-code) | [i] | ||
| 6 | Linear OOA(4204, 11790, F4, 2, 38) (dual of [(11790, 2), 23376, 39]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 7 | Linear OOA(4204, 11790, F4, 3, 38) (dual of [(11790, 3), 35166, 39]-NRT-code) | [i] | ||
| 8 | Digital (166, 204, 11790)-net over F4 | [i] | ||
| 9 | Linear OA(4207, 16423, F4, 38) (dual of [16423, 16216, 39]-code) | [i] | Construction X with Varšamov Bound | |
| 10 | Linear OA(4208, 16425, F4, 38) (dual of [16425, 16217, 39]-code) | [i] | ||
| 11 | Linear OA(4209, 16427, F4, 38) (dual of [16427, 16218, 39]-code) | [i] | ||
| 12 | Linear OOA(4204, 8209, F4, 2, 38) (dual of [(8209, 2), 16214, 39]-NRT-code) | [i] | OOA Folding | |
| 13 | Linear OOA(4204, 5473, F4, 3, 38) (dual of [(5473, 3), 16215, 39]-NRT-code) | [i] | ||