Information on Result #678588
Linear OA(4254, 65598, F4, 40) (dual of [65598, 65344, 41]-code), using construction X applied to C([0,20]) ⊂ C([0,16]) based on
- linear OA(4241, 65537, F4, 41) (dual of [65537, 65296, 42]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 416−1, defining interval I = [0,20], and minimum distance d ≥ |{−20,−19,…,20}|+1 = 42 (BCH-bound) [i]
- linear OA(4193, 65537, F4, 33) (dual of [65537, 65344, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 416−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
- linear OA(413, 61, F4, 6) (dual of [61, 48, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(413, 63, F4, 6) (dual of [63, 50, 7]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
- discarding factors / shortening the dual code based on linear OA(413, 63, F4, 6) (dual of [63, 50, 7]-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(4255, 65599, F4, 40) (dual of [65599, 65344, 41]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(4258, 65602, F4, 40) (dual of [65602, 65344, 41]-code) | [i] | ||
| 3 | Linear OA(4259, 65603, F4, 40) (dual of [65603, 65344, 41]-code) | [i] | ||
| 4 | Linear OOA(4254, 51036, F4, 2, 40) (dual of [(51036, 2), 101818, 41]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 5 | Linear OOA(4254, 51036, F4, 3, 40) (dual of [(51036, 3), 152854, 41]-NRT-code) | [i] | ||
| 6 | Digital (214, 254, 51036)-net over F4 | [i] | ||
| 7 | Linear OA(4256, 65601, F4, 40) (dual of [65601, 65345, 41]-code) | [i] | Construction X with Varšamov Bound | |
| 8 | Linear OA(4257, 65603, F4, 40) (dual of [65603, 65346, 41]-code) | [i] | ||
| 9 | Linear OA(4258, 65605, F4, 40) (dual of [65605, 65347, 41]-code) | [i] | ||
| 10 | Linear OA(4259, 65607, F4, 40) (dual of [65607, 65348, 41]-code) | [i] | ||
| 11 | Linear OA(4260, 65609, F4, 40) (dual of [65609, 65349, 41]-code) | [i] | ||
| 12 | Linear OOA(4254, 32799, F4, 2, 40) (dual of [(32799, 2), 65344, 41]-NRT-code) | [i] | OOA Folding | |
| 13 | Linear OOA(4254, 21866, F4, 3, 40) (dual of [(21866, 3), 65344, 41]-NRT-code) | [i] | ||