Information on Result #548390
There is no linear OA(2196, 212, F2, 98) (dual of [212, 16, 99]-code), because residual code would yield linear OA(298, 113, F2, 49) (dual of [113, 15, 50]-code), but
- discarding factors / shortening the dual code would yield linear OA(298, 110, F2, 49) (dual of [110, 12, 50]-code), but
- 1 times truncation [i] would yield linear OA(297, 109, F2, 48) (dual of [109, 12, 49]-code), but
- construction Y1 [i] would yield
- linear OA(296, 105, F2, 48) (dual of [105, 9, 49]-code), but
- residual code [i] would yield linear OA(248, 56, F2, 24) (dual of [56, 8, 25]-code), but
- adding a parity check bit [i] would yield linear OA(249, 57, F2, 25) (dual of [57, 8, 26]-code), but
- “BJV†bound on codes from Brouwer’s database [i]
- adding a parity check bit [i] would yield linear OA(249, 57, F2, 25) (dual of [57, 8, 26]-code), but
- residual code [i] would yield linear OA(248, 56, F2, 24) (dual of [56, 8, 25]-code), but
- OA(212, 109, S2, 4), but
- discarding factors would yield OA(212, 91, S2, 4), but
- the Rao or (dual) Hamming bound shows that M ≥ 4187 > 212 [i]
- discarding factors would yield OA(212, 91, S2, 4), but
- linear OA(296, 105, F2, 48) (dual of [105, 9, 49]-code), but
- construction Y1 [i] would yield
- 1 times truncation [i] would yield linear OA(297, 109, F2, 48) (dual of [109, 12, 49]-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.