Information on Result #2277090
Linear OA(564, 15642, F5, 13) (dual of [15642, 15578, 14]-code), using 2 times code embedding in larger space based on linear OA(562, 15640, F5, 13) (dual of [15640, 15578, 14]-code), using
- construction X4 applied to C([0,6]) ⊂ C([0,5]) [i] based on
- linear OA(561, 15626, F5, 13) (dual of [15626, 15565, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 15626 | 512−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- linear OA(549, 15626, F5, 11) (dual of [15626, 15577, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 15626 | 512−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- linear OA(513, 14, F5, 13) (dual of [14, 1, 14]-code or 14-arc in PG(12,5)), using
- dual of repetition code with length 14 [i]
- linear OA(51, 14, F5, 1) (dual of [14, 13, 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(564, 12356, F5, 2, 13) (dual of [(12356, 2), 24648, 14]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(564, 12356, F5, 3, 13) (dual of [(12356, 3), 37004, 14]-NRT-code) | [i] | ||
| 3 | Digital (51, 64, 12356)-net over F5 | [i] | ||
| 4 | Linear OOA(564, 5214, F5, 3, 13) (dual of [(5214, 3), 15578, 14]-NRT-code) | [i] | OOA Folding | |