Information on Result #1307710
Linear OA(477, 1072, F4, 19) (dual of [1072, 995, 20]-code), using 31 step Varšamov–Edel lengthening with (ri) = (2, 0, 1, 0, 0, 0, 1, 7 times 0, 1, 16 times 0) based on linear OA(472, 1036, F4, 19) (dual of [1036, 964, 20]-code), using
- construction X applied to C([0,9]) ⊂ C([0,8]) [i] 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: 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(477, 1072, F4, 2, 19) (dual of [(1072, 2), 2067, 20]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(477, 1072, F4, 3, 19) (dual of [(1072, 3), 3139, 20]-NRT-code) | [i] | ||
| 3 | Digital (58, 77, 1072)-net over F4 | [i] | ||