Information on Result #678601
Linear OA(4158, 65598, F4, 24) (dual of [65598, 65440, 25]-code), using construction X applied to C([0,12]) ⊂ C([0,8]) based on
- linear OA(4145, 65537, F4, 25) (dual of [65537, 65392, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 416−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(497, 65537, F4, 17) (dual of [65537, 65440, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 416−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (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(4159, 65599, F4, 24) (dual of [65599, 65440, 25]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(4158, 59721, F4, 2, 24) (dual of [(59721, 2), 119284, 25]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(4158, 59721, F4, 3, 24) (dual of [(59721, 3), 179005, 25]-NRT-code) | [i] | ||
| 4 | Digital (134, 158, 59721)-net over F4 | [i] | ||
| 5 | Linear OA(4160, 65601, F4, 24) (dual of [65601, 65441, 25]-code) | [i] | Construction X with Varšamov Bound | |
| 6 | Linear OA(4161, 65603, F4, 24) (dual of [65603, 65442, 25]-code) | [i] | ||
| 7 | Linear OOA(4158, 32799, F4, 2, 24) (dual of [(32799, 2), 65440, 25]-NRT-code) | [i] | OOA Folding | |
| 8 | Linear OOA(4158, 21866, F4, 3, 24) (dual of [(21866, 3), 65440, 25]-NRT-code) | [i] | ||
| 9 | Linear OOA(4158, 5466, F4, 24, 24) (dual of [(5466, 24), 131026, 25]-NRT-code) | [i] | OA Folding and Stacking | |