MinT - Information on Result #552190

Information on Result #552190

There is no linear OOA(2¹⁵², 222, F₂, 2, 71) (dual of [(222, 2), 292, 72]-NRT-code), because 1 step m-reduction would yield linear OA(2¹⁵¹, 222, F₂, 70) (dual of [222, 71, 71]-code), but

constructionÂ Y1 [i] would yield
1. linear OA(2¹⁵⁰, 194, F₂, 70) (dual of [194, 44, 71]-code), but
  - constructionÂ Y1 [i] would yield
    1. linear OA(2¹⁴⁹, 178, F₂, 70) (dual of [178, 29, 71]-code), but
      - adding a parity check bit [i] would yield linear OA(2¹⁵⁰, 179, F₂, 71) (dual of [179, 29, 72]-code), but
        â€œBKâ€ bound on codes from Brouwerâ€™s database [i]
    2. OA(2⁴⁴, 194, S₂, 16), but
      - discarding factors would yield OA(2⁴⁴, 173, S₂, 16), but
        the Rao or (dual) Hamming bound shows that MÂ â‰¥ 17 734855 699135 > 2⁴⁴ [i]
2. OA(2⁷¹, 222, S₂, 28), but
  - discarding factors would yield OA(2⁷¹, 209, S₂, 28), but
    - the Rao or (dual) Hamming bound shows that MÂ â‰¥ 2400 648072 841355 873622 > 2⁷¹ [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(2¹⁵², 222, F₂, 3, 71) (dual of [(222, 3), 514, 72]-NRT-code)	[i]	Depth Reduction
2	No linear OOA(2¹⁵², 222, F₂, 4, 71) (dual of [(222, 4), 736, 72]-NRT-code)	[i]
3	No linear OOA(2¹⁵², 222, F₂, 5, 71) (dual of [(222, 5), 958, 72]-NRT-code)	[i]
4	No linear OOA(2¹⁵², 222, F₂, 6, 71) (dual of [(222, 6), 1180, 72]-NRT-code)	[i]
5	No linear OOA(2¹⁵², 222, F₂, 7, 71) (dual of [(222, 7), 1402, 72]-NRT-code)	[i]
6	No linear OOA(2¹⁵², 222, F₂, 8, 71) (dual of [(222, 8), 1624, 72]-NRT-code)	[i]