Information on Result #678580
Linear OA(4152, 65576, F4, 24) (dual of [65576, 65424, 25]-code), using construction X applied to C([0,12]) ⊂ C([0,9]) 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(4113, 65537, F4, 19) (dual of [65537, 65424, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 416−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(47, 39, F4, 4) (dual of [39, 32, 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(4153, 65577, F4, 24) (dual of [65577, 65424, 25]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(4152, 40914, F4, 2, 24) (dual of [(40914, 2), 81676, 25]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(4152, 40914, F4, 3, 24) (dual of [(40914, 3), 122590, 25]-NRT-code) | [i] | ||
| 4 | Digital (128, 152, 40914)-net over F4 | [i] | ||
| 5 | Linear OA(4154, 65579, F4, 24) (dual of [65579, 65425, 25]-code) | [i] | Construction X with Varšamov Bound | |
| 6 | Linear OOA(4152, 32788, F4, 2, 24) (dual of [(32788, 2), 65424, 25]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(4152, 21858, F4, 3, 24) (dual of [(21858, 3), 65422, 25]-NRT-code) | [i] | ||
| 8 | Linear OOA(4152, 5464, F4, 24, 24) (dual of [(5464, 24), 130984, 25]-NRT-code) | [i] | OA Folding and Stacking | |