Information on Result #548078
There is no linear OA(831, 65, F8, 27) (dual of [65, 34, 28]-code), because construction Y1 would yield
- linear OA(830, 35, F8, 27) (dual of [35, 5, 28]-code), but
- construction Y1 [i] would yield
- OA(829, 31, S8, 27), but
- 3 times truncation [i] would yield OA(826, 28, S8, 24), but
- the (dual) Plotkin bound shows that M ≥ 9 671406 556917 033397 649408 / 25 > 826 [i]
- 3 times truncation [i] would yield OA(826, 28, S8, 24), but
- OA(85, 35, S8, 4), but
- the linear programming bound shows that M ≥ 1 306624 / 39 > 85 [i]
- OA(829, 31, S8, 27), but
- construction Y1 [i] would yield
- linear OA(834, 65, F8, 30) (dual of [65, 31, 31]-code), but
- discarding factors / shortening the dual code would yield linear OA(834, 59, F8, 30) (dual of [59, 25, 31]-code), but
- construction Y1 [i] would yield
- OA(833, 37, S8, 30), but
- the linear programming bound shows that M ≥ 299 165541 653862 138753 221956 468736 / 465 > 833 [i]
- linear OA(825, 59, F8, 22) (dual of [59, 34, 23]-code), but
- discarding factors / shortening the dual code would yield linear OA(825, 52, F8, 22) (dual of [52, 27, 23]-code), but
- construction Y1 [i] would yield
- OA(824, 28, S8, 22), but
- the linear programming bound shows that M ≥ 41 859056 504156 535174 201344 / 8073 > 824 [i]
- linear OA(827, 52, F8, 24) (dual of [52, 25, 25]-code), but
- discarding factors / shortening the dual code would yield linear OA(827, 36, F8, 24) (dual of [36, 9, 25]-code), but
- residual code [i] would yield OA(83, 11, S8, 3), but
- 1 times truncation [i] would yield OA(82, 10, S8, 2), but
- bound for OAs with strength k = 2 [i]
- the Rao or (dual) Hamming bound shows that M ≥ 71 > 82 [i]
- 1 times truncation [i] would yield OA(82, 10, S8, 2), but
- residual code [i] would yield OA(83, 11, S8, 3), but
- discarding factors / shortening the dual code would yield linear OA(827, 36, F8, 24) (dual of [36, 9, 25]-code), but
- OA(824, 28, S8, 22), but
- construction Y1 [i] would yield
- discarding factors / shortening the dual code would yield linear OA(825, 52, F8, 22) (dual of [52, 27, 23]-code), but
- OA(833, 37, S8, 30), but
- construction Y1 [i] would yield
- discarding factors / shortening the dual code would yield linear OA(834, 59, F8, 30) (dual of [59, 25, 31]-code), but
Mode: Bound (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
None.