Information on Result #2277093
Linear OA(574, 78144, F5, 13) (dual of [78144, 78070, 14]-code), using 2 times code embedding in larger space based on linear OA(572, 78142, F5, 13) (dual of [78142, 78070, 14]-code), using
- construction X4 applied to C([0,6]) ⊂ C([0,5]) [i] based on
- 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(557, 78126, F5, 11) (dual of [78126, 78069, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 78126 | 514−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (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(574, 53397, F5, 2, 13) (dual of [(53397, 2), 106720, 14]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(574, 53397, F5, 3, 13) (dual of [(53397, 3), 160117, 14]-NRT-code) | [i] | ||
| 3 | Digital (61, 74, 53397)-net over F5 | [i] | ||
| 4 | Linear OOA(574, 26048, F5, 3, 13) (dual of [(26048, 3), 78070, 14]-NRT-code) | [i] | OOA Folding | |