Information on Result #2277199
Linear OA(587, 78143, F5, 15) (dual of [78143, 78056, 16]-code), using 1 times code embedding in larger space based on linear OA(586, 78142, F5, 15) (dual of [78142, 78056, 16]-code), using
- construction X4 applied to C([0,7]) ⊂ C([0,6]) [i] based on
- linear OA(585, 78126, F5, 15) (dual of [78126, 78041, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 78126 | 514−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- linear OA(571, 78126, F5, 13) (dual of [78126, 78055, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 78126 | 514−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- linear OA(515, 16, F5, 15) (dual of [16, 1, 16]-code or 16-arc in PG(14,5)), using
- dual of repetition code with length 16 [i]
- linear OA(51, 16, F5, 1) (dual of [16, 15, 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(587, 59599, F5, 2, 15) (dual of [(59599, 2), 119111, 16]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(587, 59599, F5, 3, 15) (dual of [(59599, 3), 178710, 16]-NRT-code) | [i] | ||
| 3 | Digital (72, 87, 59599)-net over F5 | [i] | ||