Information on Result #678564
Linear OA(4248, 65576, F4, 40) (dual of [65576, 65328, 41]-code), using construction X applied to C([0,20]) ⊂ C([0,17]) 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(4209, 65537, F4, 35) (dual of [65537, 65328, 36]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 416−1, defining interval I = [0,17], and minimum distance d ≥ |{−17,−16,…,17}|+1 = 36 (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(4249, 65577, F4, 40) (dual of [65577, 65328, 41]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(4248, 40997, F4, 2, 40) (dual of [(40997, 2), 81746, 41]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(4248, 40997, F4, 3, 40) (dual of [(40997, 3), 122743, 41]-NRT-code) | [i] | ||
| 4 | Digital (208, 248, 40997)-net over F4 | [i] | ||
| 5 | Linear OOA(4248, 32788, F4, 2, 40) (dual of [(32788, 2), 65328, 41]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(4248, 21858, F4, 3, 40) (dual of [(21858, 3), 65326, 41]-NRT-code) | [i] | ||