Information on Result #2277149
Linear OA(580, 78142, F5, 14) (dual of [78142, 78062, 15]-code), using 1 times code embedding in larger space based on linear OA(579, 78141, F5, 14) (dual of [78141, 78062, 15]-code), using
- construction X4 applied to Ce(13) ⊂ Ce(11) [i] based on
- linear OA(578, 78125, F5, 14) (dual of [78125, 78047, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(564, 78125, F5, 12) (dual of [78125, 78061, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [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(580, 52819, F5, 2, 14) (dual of [(52819, 2), 105558, 15]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(580, 52819, F5, 3, 14) (dual of [(52819, 3), 158377, 15]-NRT-code) | [i] | ||
| 3 | Digital (66, 80, 52819)-net over F5 | [i] | ||
| 4 | Linear OOA(580, 39071, F5, 2, 14) (dual of [(39071, 2), 78062, 15]-NRT-code) | [i] | OOA Folding | |