Information on Result #560906
There is no linear OOA(4220, 231, F4, 2, 165) (dual of [(231, 2), 242, 166]-NRT-code), because 1 step m-reduction would yield linear OA(4219, 231, F4, 164) (dual of [231, 12, 165]-code), but
- construction Y1 [i] would yield
- linear OA(4218, 225, F4, 164) (dual of [225, 7, 165]-code), but
- residual code [i] would yield linear OA(454, 60, F4, 41) (dual of [60, 6, 42]-code), but
- 1 times truncation [i] would yield linear OA(453, 59, F4, 40) (dual of [59, 6, 41]-code), but
- residual code [i] would yield linear OA(413, 18, F4, 10) (dual of [18, 5, 11]-code), but
- “Liz†bound on codes from Brouwer’s database [i]
- residual code [i] would yield linear OA(413, 18, F4, 10) (dual of [18, 5, 11]-code), but
- 1 times truncation [i] would yield linear OA(453, 59, F4, 40) (dual of [59, 6, 41]-code), but
- residual code [i] would yield linear OA(454, 60, F4, 41) (dual of [60, 6, 42]-code), but
- OA(412, 231, S4, 6), but
- discarding factors would yield OA(412, 156, S4, 6), but
- the Rao or (dual) Hamming bound shows that M ≥ 16 866019 > 412 [i]
- discarding factors would yield OA(412, 156, S4, 6), but
- linear OA(4218, 225, F4, 164) (dual of [225, 7, 165]-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.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | No linear OOA(4220, 231, F4, 3, 165) (dual of [(231, 3), 473, 166]-NRT-code) | [i] | Depth Reduction | |