Information on Result #698063
Linear OA(4923, 5764815, F49, 6) (dual of [5764815, 5764792, 7]-code), using construction X applied to Ce(5) ⊂ Ce(2) based on
- linear OA(4921, 5764801, F49, 6) (dual of [5764801, 5764780, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 494−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(499, 5764801, F49, 3) (dual of [5764801, 5764792, 4]-code or 5764801-cap in PG(8,49)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 494−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [i]
- linear OA(492, 14, F49, 2) (dual of [14, 12, 3]-code or 14-arc in PG(1,49)), using
- discarding factors / shortening the dual code based on linear OA(492, 49, F49, 2) (dual of [49, 47, 3]-code or 49-arc in PG(1,49)), using
- Reed–Solomon code RS(47,49) [i]
- discarding factors / shortening the dual code based on linear OA(492, 49, F49, 2) (dual of [49, 47, 3]-code or 49-arc in PG(1,49)), 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(4923, 5764815, F49, 2, 6) (dual of [(5764815, 2), 11529607, 7]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4923, 5764815, F49, 3, 6) (dual of [(5764815, 3), 17294422, 7]-NRT-code) | [i] | ||
| 3 | Digital (17, 23, 5764815)-net over F49 | [i] | ||
| 4 | Linear OOA(4923, 2882407, F49, 2, 6) (dual of [(2882407, 2), 5764791, 7]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(4923, 1921605, F49, 3, 6) (dual of [(1921605, 3), 5764792, 7]-NRT-code) | [i] | ||
| 6 | Linear OOA(4923, 1921605, F49, 6, 6) (dual of [(1921605, 6), 11529607, 7]-NRT-code) | [i] | OA Folding and Stacking | |