MinT - Information on Result #552364

Information on Result #552364

There is no linear OOA(2¹⁵⁹, 190, F₂, 2, 77) (dual of [(190, 2), 221, 78]-NRT-code), because 3 step m-reduction would yield linear OA(2¹⁵⁶, 190, F₂, 74) (dual of [190, 34, 75]-code), but

constructionÂ Y1 [i] would yield
1. linear OA(2¹⁵⁵, 178, F₂, 74) (dual of [178, 23, 75]-code), but
  - adding a parity check bit [i] would yield linear OA(2¹⁵⁶, 179, F₂, 75) (dual of [179, 23, 76]-code), but
    - â€œBKâ€ bound on codes from Brouwerâ€™s database [i]
2. OA(2³⁴, 190, S₂, 12), but
  - discarding factors would yield OA(2³⁴, 154, S₂, 12), but
    - the Rao or (dual) Hamming bound shows that MÂ â‰¥ 17486 314616 > 2³⁴ [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(2¹⁵⁹, 190, F₂, 3, 77) (dual of [(190, 3), 411, 78]-NRT-code)	[i]	Depth Reduction
2	No linear OOA(2¹⁵⁹, 190, F₂, 4, 77) (dual of [(190, 4), 601, 78]-NRT-code)	[i]
3	No linear OOA(2¹⁵⁹, 190, F₂, 5, 77) (dual of [(190, 5), 791, 78]-NRT-code)	[i]
4	No linear OOA(2¹⁵⁹, 190, F₂, 6, 77) (dual of [(190, 6), 981, 78]-NRT-code)	[i]
5	No linear OOA(2¹⁵⁹, 190, F₂, 7, 77) (dual of [(190, 7), 1171, 78]-NRT-code)	[i]
6	No linear OOA(2¹⁵⁹, 190, F₂, 8, 77) (dual of [(190, 8), 1361, 78]-NRT-code)	[i]