Information on Result #576658
There is no linear OOA(722, 35, F7, 3, 19) (dual of [(35, 3), 83, 20]-NRT-code), because 1 times depth reduction would yield linear OOA(722, 35, F7, 2, 19) (dual of [(35, 2), 48, 20]-NRT-code), but
- 1 step m-reduction [i] would yield linear OA(721, 35, F7, 18) (dual of [35, 14, 19]-code), but
- construction Y1 [i] would yield
- linear OA(720, 23, F7, 18) (dual of [23, 3, 19]-code), but
- “Hi4†bound on codes from Brouwer’s database [i]
- linear OA(714, 35, F7, 12) (dual of [35, 21, 13]-code), but
- discarding factors / shortening the dual code would yield linear OA(714, 30, F7, 12) (dual of [30, 16, 13]-code), but
- construction Y1 [i] would yield
- linear OA(713, 16, F7, 12) (dual of [16, 3, 13]-code), but
- linear OA(716, 30, F7, 14) (dual of [30, 14, 15]-code), but
- discarding factors / shortening the dual code would yield linear OA(716, 24, F7, 14) (dual of [24, 8, 15]-code), but
- residual code [i] would yield OA(72, 9, S7, 2), but
- bound for OAs with strength k = 2 [i]
- the Rao or (dual) Hamming bound shows that M ≥ 55 > 72 [i]
- residual code [i] would yield OA(72, 9, S7, 2), but
- discarding factors / shortening the dual code would yield linear OA(716, 24, F7, 14) (dual of [24, 8, 15]-code), but
- construction Y1 [i] would yield
- discarding factors / shortening the dual code would yield linear OA(714, 30, F7, 12) (dual of [30, 16, 13]-code), but
- linear OA(720, 23, F7, 18) (dual of [23, 3, 19]-code), but
- construction Y1 [i] would yield
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.
Other Results with Identical Parameters
None.
Depending Results
None.