Information on Result #698062
Linear OA(4927, 5764815, F49, 7) (dual of [5764815, 5764788, 8]-code), using construction X applied to Ce(6) ⊂ Ce(3) based on
- linear OA(4925, 5764801, F49, 7) (dual of [5764801, 5764776, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 494−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(4913, 5764801, F49, 4) (dual of [5764801, 5764788, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 494−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [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(4927, 5764815, F49, 2, 7) (dual of [(5764815, 2), 11529603, 8]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4927, 5764815, F49, 3, 7) (dual of [(5764815, 3), 17294418, 8]-NRT-code) | [i] | ||
| 3 | Digital (20, 27, 5764815)-net over F49 | [i] | ||
| 4 | Linear OOA(4927, 2882407, F49, 2, 7) (dual of [(2882407, 2), 5764787, 8]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(4927, 1921605, F49, 3, 7) (dual of [(1921605, 3), 5764788, 8]-NRT-code) | [i] | ||
| 6 | Linear OOA(4927, 1921604, F49, 7, 7) (dual of [(1921604, 7), 13451201, 8]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |