MinT - Information on Result #553070

Information on Result #553070

There is no linear OOA(2¹⁸⁴, 225, F₂, 2, 87) (dual of [(225, 2), 266, 88]-NRT-code), because 1 step m-reduction would yield linear OA(2¹⁸³, 225, F₂, 86) (dual of [225, 42, 87]-code), but

constructionÂ Y1 [i] would yield
1. linear OA(2¹⁸², 211, F₂, 86) (dual of [211, 29, 87]-code), but
  - adding a parity check bit [i] would yield linear OA(2¹⁸³, 212, F₂, 87) (dual of [212, 29, 88]-code), but
    - â€œBKâ€ bound on codes from Brouwerâ€™s database [i]
2. OA(2⁴², 225, S₂, 14), but
  - discarding factors would yield OA(2⁴², 219, S₂, 14), but
    - the Rao or (dual) Hamming bound shows that MÂ â‰¥ 4 498367 189624 > 2⁴² [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(2¹⁸⁴, 225, F₂, 3, 87) (dual of [(225, 3), 491, 88]-NRT-code)	[i]	Depth Reduction
2	No linear OOA(2¹⁸⁴, 225, F₂, 4, 87) (dual of [(225, 4), 716, 88]-NRT-code)	[i]
3	No linear OOA(2¹⁸⁴, 225, F₂, 5, 87) (dual of [(225, 5), 941, 88]-NRT-code)	[i]
4	No linear OOA(2¹⁸⁴, 225, F₂, 6, 87) (dual of [(225, 6), 1166, 88]-NRT-code)	[i]
5	No linear OOA(2¹⁸⁴, 225, F₂, 7, 87) (dual of [(225, 7), 1391, 88]-NRT-code)	[i]
6	No linear OOA(2¹⁸⁴, 225, F₂, 8, 87) (dual of [(225, 8), 1616, 88]-NRT-code)	[i]