MinT - Information on Result #553437

Information on Result #553437

There is no linear OOA(2¹⁹⁶, 232, F₂, 2, 93) (dual of [(232, 2), 268, 94]-NRT-code), because 1 step m-reduction would yield linear OA(2¹⁹⁵, 232, F₂, 92) (dual of [232, 37, 93]-code), but

constructionÂ Y1 [i] would yield
1. linear OA(2¹⁹⁴, 220, F₂, 92) (dual of [220, 26, 93]-code), but
  - adding a parity check bit [i] would yield linear OA(2¹⁹⁵, 221, F₂, 93) (dual of [221, 26, 94]-code), but
    - â€œBKâ€ bound on codes from Brouwerâ€™s database [i]
2. OA(2³⁷, 232, S₂, 12), but
  - discarding factors would yield OA(2³⁷, 217, S₂, 12), but
    - the Rao or (dual) Hamming bound shows that MÂ â‰¥ 139173 045698 > 2³⁷ [i]

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		Method
1	No linear OOA(2¹⁹⁶, 232, F₂, 3, 93) (dual of [(232, 3), 500, 94]-NRT-code)	[i]	Depth Reduction
2	No linear OOA(2¹⁹⁶, 232, F₂, 4, 93) (dual of [(232, 4), 732, 94]-NRT-code)	[i]
3	No linear OOA(2¹⁹⁶, 232, F₂, 5, 93) (dual of [(232, 5), 964, 94]-NRT-code)	[i]
4	No linear OOA(2¹⁹⁶, 232, F₂, 6, 93) (dual of [(232, 6), 1196, 94]-NRT-code)	[i]
5	No linear OOA(2¹⁹⁶, 232, F₂, 7, 93) (dual of [(232, 7), 1428, 94]-NRT-code)	[i]
6	No linear OOA(2¹⁹⁶, 232, F₂, 8, 93) (dual of [(232, 8), 1660, 94]-NRT-code)	[i]