Information on Result #944608
Linear OOA(726, 5764803, F7, 3, 4) (dual of [(5764803, 3), 17294383, 5]-NRT-code), using OOA stacking with additional row based on linear OOA(726, 5764804, F7, 2, 4) (dual of [(5764804, 2), 11529582, 5]-NRT-code), using
- trace code [i] based on 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, k and s, k and t, m and s, m 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(7102, 7686862, F7, 3, 9) (dual of [(7686862, 3), 23060484, 10]-NRT-code) | [i] | Generalized (u, u+v)-Construction for OOAs | |
| 2 | Linear OOA(7103, 7688927, F7, 3, 9) (dual of [(7688927, 3), 23066678, 10]-NRT-code) | [i] | ||
| 3 | Linear OOA(792, 7686632, F7, 3, 8) (dual of [(7686632, 3), 23059804, 9]-NRT-code) | [i] | ||
| 4 | Linear OOA(792, 7686828, F7, 3, 8) (dual of [(7686828, 3), 23060392, 9]-NRT-code) | [i] | ||
| 5 | Linear OOA(7101, 7686650, F7, 3, 9) (dual of [(7686650, 3), 23059849, 10]-NRT-code) | [i] | ||
| 6 | Linear OOA(7101, 7686854, F7, 3, 9) (dual of [(7686854, 3), 23060461, 10]-NRT-code) | [i] | ||
| 7 | Linear OOA(7102, 7686952, F7, 3, 9) (dual of [(7686952, 3), 23060754, 10]-NRT-code) | [i] | ||
| 8 | Linear OOA(7102, 7688919, F7, 3, 9) (dual of [(7688919, 3), 23066655, 10]-NRT-code) | [i] | ||
| 9 | Linear OOA(7103, 7689017, F7, 3, 9) (dual of [(7689017, 3), 23066948, 10]-NRT-code) | [i] | ||
| 10 | Linear OOA(7103, 7692892, F7, 3, 9) (dual of [(7692892, 3), 23078573, 10]-NRT-code) | [i] | ||
| 11 | Linear OOA(790, 7686477, F7, 3, 8) (dual of [(7686477, 3), 23059341, 9]-NRT-code) | [i] | ||
| 12 | Linear OOA(791, 7686575, F7, 3, 8) (dual of [(7686575, 3), 23059634, 9]-NRT-code) | [i] | ||
| 13 | Linear OOA(791, 7686820, F7, 3, 8) (dual of [(7686820, 3), 23060369, 9]-NRT-code) | [i] | ||
| 14 | Linear OOA(798, 7686462, F7, 3, 9) (dual of [(7686462, 3), 23059288, 10]-NRT-code) | [i] | ||
| 15 | Linear OOA(799, 7686544, F7, 3, 9) (dual of [(7686544, 3), 23059533, 10]-NRT-code) | [i] | ||
| 16 | Linear OOA(7100, 7686846, F7, 3, 9) (dual of [(7686846, 3), 23060438, 10]-NRT-code) | [i] | ||
| 17 | Linear OOA(7101, 7686895, F7, 3, 9) (dual of [(7686895, 3), 23060584, 10]-NRT-code) | [i] | ||
| 18 | Linear OOA(7101, 7688911, F7, 3, 9) (dual of [(7688911, 3), 23066632, 10]-NRT-code) | [i] | ||
| 19 | Linear OOA(7102, 7688960, F7, 3, 9) (dual of [(7688960, 3), 23066778, 10]-NRT-code) | [i] | ||
| 20 | Linear OOA(7102, 7692884, F7, 3, 9) (dual of [(7692884, 3), 23078550, 10]-NRT-code) | [i] | ||
| 21 | Linear OOA(7103, 7692933, F7, 3, 9) (dual of [(7692933, 3), 23078696, 10]-NRT-code) | [i] | ||
| 22 | Linear OOA(7103, 7707967, F7, 3, 9) (dual of [(7707967, 3), 23123798, 10]-NRT-code) | [i] | ||
| 23 | Linear OOA(789, 7686469, F7, 3, 8) (dual of [(7686469, 3), 23059318, 9]-NRT-code) | [i] | ||
| 24 | Linear OOA(790, 7686518, F7, 3, 8) (dual of [(7686518, 3), 23059464, 9]-NRT-code) | [i] | ||
| 25 | Linear OOA(790, 7686812, F7, 3, 8) (dual of [(7686812, 3), 23060346, 9]-NRT-code) | [i] | ||
| 26 | Linear OOA(796, 7686454, F7, 3, 9) (dual of [(7686454, 3), 23059266, 10]-NRT-code) | [i] | ||
| 27 | Linear OOA(797, 7686536, F7, 3, 9) (dual of [(7686536, 3), 23059511, 10]-NRT-code) | [i] | ||
| 28 | Linear OOA(798, 7686838, F7, 3, 9) (dual of [(7686838, 3), 23060416, 10]-NRT-code) | [i] | ||
| 29 | Linear OOA(799, 7688903, F7, 3, 9) (dual of [(7688903, 3), 23066610, 10]-NRT-code) | [i] | ||
| 30 | Linear OOA(7100, 7692876, F7, 3, 9) (dual of [(7692876, 3), 23078528, 10]-NRT-code) | [i] | ||
| 31 | Linear OOA(7101, 7707959, F7, 3, 9) (dual of [(7707959, 3), 23123776, 10]-NRT-code) | [i] | ||
| 32 | Linear OOA(787, 7686461, F7, 3, 8) (dual of [(7686461, 3), 23059296, 9]-NRT-code) | [i] | ||
| 33 | Linear OOA(788, 7686804, F7, 3, 8) (dual of [(7686804, 3), 23060324, 9]-NRT-code) | [i] | ||