Information on Result #680123
Linear OA(472, 1036, F4, 19) (dual of [1036, 964, 20]-code), using construction X applied to C([0,9]) ⊂ C([0,8]) based on
- linear OA(471, 1025, F4, 19) (dual of [1025, 954, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 1025 | 410−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(461, 1025, F4, 17) (dual of [1025, 964, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 1025 | 410−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(41, 11, F4, 1) (dual of [11, 10, 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 OOA(472, 770, F4, 2, 19) (dual of [(770, 2), 1468, 20]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(472, 770, F4, 3, 19) (dual of [(770, 3), 2238, 20]-NRT-code) | [i] | ||
| 3 | Digital (53, 72, 770)-net over F4 | [i] | ||
| 4 | Linear OA(476, 1054, F4, 19) (dual of [1054, 978, 20]-code) | [i] | Varšamov–Edel Lengthening | |
| 5 | Linear OA(477, 1072, F4, 19) (dual of [1072, 995, 20]-code) | [i] | ||
| 6 | Linear OA(479, 1151, F4, 19) (dual of [1151, 1072, 20]-code) | [i] | ||
| 7 | Linear OOA(472, 518, F4, 2, 19) (dual of [(518, 2), 964, 20]-NRT-code) | [i] | OOA Folding | |
| 8 | Linear OOA(472, 345, F4, 3, 19) (dual of [(345, 3), 963, 20]-NRT-code) | [i] | ||