Information on Result #679024
Linear OA(4212, 16392, F4, 41) (dual of [16392, 16180, 42]-code), using construction X applied to Ce(40) ⊂ Ce(38) based on
- linear OA(4211, 16384, F4, 41) (dual of [16384, 16173, 42]-code), using an extension Ce(40) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,40], and designed minimum distance d ≥ |I|+1 = 41 [i]
- 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(41, 8, F4, 1) (dual of [8, 7, 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(4211, 16391, F4, 40) (dual of [16391, 16180, 41]-code) | [i] | Truncation | |
| 2 | Linear OOA(4212, 9250, F4, 2, 41) (dual of [(9250, 2), 18288, 42]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(4212, 9250, F4, 3, 41) (dual of [(9250, 3), 27538, 42]-NRT-code) | [i] | ||
| 4 | Digital (171, 212, 9250)-net over F4 | [i] | ||
| 5 | Linear OOA(4212, 8196, F4, 2, 41) (dual of [(8196, 2), 16180, 42]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(4212, 5464, F4, 3, 41) (dual of [(5464, 3), 16180, 42]-NRT-code) | [i] | ||