Information on Result #903100
Linear OOA(4915, 2882452, F49, 2, 4) (dual of [(2882452, 2), 5764889, 5]-NRT-code), using (u, u+v)-construction based on
- linear OOA(492, 50, F49, 2, 2) (dual of [(50, 2), 98, 3]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(2;98,49) [i]
- linear OOA(4913, 2882402, F49, 2, 4) (dual of [(2882402, 2), 5764791, 5]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4913, 5764804, F49, 4) (dual of [5764804, 5764791, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(4913, 5764805, F49, 4) (dual of [5764805, 5764792, 5]-code), using
- construction X applied to Ce(3) ⊂ Ce(2) [i] based on
- 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(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(490, 4, F49, 0) (dual of [4, 4, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(490, s, F49, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(3) ⊂ Ce(2) [i] based on
- discarding factors / shortening the dual code based on linear OA(4913, 5764805, F49, 4) (dual of [5764805, 5764792, 5]-code), using
- OOA 2-folding [i] based on linear OA(4913, 5764804, F49, 4) (dual of [5764804, 5764791, 5]-code), 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(4920, 5764904, F49, 2, 4) (dual of [(5764904, 2), 11529788, 5]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |
| 2 | Linear OOA(4946, 5764814, F49, 2, 8) (dual of [(5764814, 2), 11529582, 9]-NRT-code) | [i] | ||
| 3 | Linear OOA(4947, 5764820, F49, 2, 8) (dual of [(5764820, 2), 11529593, 9]-NRT-code) | [i] | ||
| 4 | Linear OOA(4948, 5764904, F49, 2, 8) (dual of [(5764904, 2), 11529760, 9]-NRT-code) | [i] | ||
| 5 | Linear OOA(4949, 5764907, F49, 2, 8) (dual of [(5764907, 2), 11529765, 9]-NRT-code) | [i] | ||
| 6 | Linear OOA(4950, 5766030, F49, 2, 8) (dual of [(5766030, 2), 11532010, 9]-NRT-code) | [i] | ||
| 7 | Linear OOA(4951, 7076753, F49, 2, 8) (dual of [(7076753, 2), 14153455, 9]-NRT-code) | [i] | ||
| 8 | Linear OOA(4949, 5764812, F49, 2, 9) (dual of [(5764812, 2), 11529575, 10]-NRT-code) | [i] | ||
| 9 | Linear OOA(4950, 5764814, F49, 2, 9) (dual of [(5764814, 2), 11529578, 10]-NRT-code) | [i] | ||
| 10 | Linear OOA(4951, 5764820, F49, 2, 9) (dual of [(5764820, 2), 11529589, 10]-NRT-code) | [i] | ||
| 11 | Linear OOA(4952, 5764904, F49, 2, 9) (dual of [(5764904, 2), 11529756, 10]-NRT-code) | [i] | ||
| 12 | Linear OOA(4953, 5764908, F49, 2, 9) (dual of [(5764908, 2), 11529763, 10]-NRT-code) | [i] | ||
| 13 | Linear OOA(4954, 5766030, F49, 2, 9) (dual of [(5766030, 2), 11532006, 10]-NRT-code) | [i] | ||
| 14 | Linear OOA(4915, 2882451, F49, 3, 4) (dual of [(2882451, 3), 8647338, 5]-NRT-code) | [i] | OOA Stacking with Additional Row | |