Information on Result #2277097
Linear OA(594, 1953148, F5, 13) (dual of [1953148, 1953054, 14]-code), using 2 times code embedding in larger space based on linear OA(592, 1953146, F5, 13) (dual of [1953146, 1953054, 14]-code), using
- construction X4 applied to C([0,6]) ⊂ C([0,5]) [i] based on
- linear OA(591, 1953126, F5, 13) (dual of [1953126, 1953035, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 1953126 | 518−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- linear OA(573, 1953126, F5, 11) (dual of [1953126, 1953053, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 1953126 | 518−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- linear OA(519, 20, F5, 19) (dual of [20, 1, 20]-code or 20-arc in PG(18,5)), using
- dual of repetition code with length 20 [i]
- linear OA(51, 20, F5, 1) (dual of [20, 19, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(51, s, F5, 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(594, 996379, F5, 2, 13) (dual of [(996379, 2), 1992664, 14]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(594, 996379, F5, 3, 13) (dual of [(996379, 3), 2989043, 14]-NRT-code) | [i] | ||
| 3 | Digital (81, 94, 996379)-net over F5 | [i] | ||