Information on Result #638571
Linear OA(786, 100, F7, 56) (dual of [100, 14, 57]-code), using concatenation of two codes based on
- linear OA(4918, 25, F49, 18) (dual of [25, 7, 19]-code or 25-arc in PG(17,49)), using
- discarding factors / shortening the dual code based on linear OA(4918, 49, F49, 18) (dual of [49, 31, 19]-code or 49-arc in PG(17,49)), using
- Reed–Solomon code RS(31,49) [i]
- discarding factors / shortening the dual code based on linear OA(4918, 49, F49, 18) (dual of [49, 31, 19]-code or 49-arc in PG(17,49)), using
- linear OA(72, 4, F7, 2) (dual of [4, 2, 3]-code or 4-arc in PG(1,7)), using
- discarding factors / shortening the dual code based on linear OA(72, 7, F7, 2) (dual of [7, 5, 3]-code or 7-arc in PG(1,7)), using
- Reed–Solomon code RS(5,7) [i]
- discarding factors / shortening the dual code based on linear OA(72, 7, F7, 2) (dual of [7, 5, 3]-code or 7-arc in PG(1,7)), 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.
Compare with Markus Grassl’s online database of code parameters.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OA(786, 100, F7, 55) (dual of [100, 14, 56]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(785, 99, F7, 55) (dual of [99, 14, 56]-code) | [i] | Truncation | |
| 3 | Linear OA(784, 98, F7, 54) (dual of [98, 14, 55]-code) | [i] | ||
| 4 | Linear OA(783, 97, F7, 53) (dual of [97, 14, 54]-code) | [i] | ||
| 5 | Linear OA(781, 95, F7, 51) (dual of [95, 14, 52]-code) | [i] | ||
| 6 | Linear OOA(786, 50, F7, 2, 56) (dual of [(50, 2), 14, 57]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(786, 33, F7, 3, 56) (dual of [(33, 3), 13, 57]-NRT-code) | [i] | ||