MinT - Information on Result #548530

Information on Result #548530

There is no linear OA(2¹¹, 58, F₂, 4) (dual of [58, 47, 5]-code), because constructionÂ Y1 would yield

linear OA(2¹⁰, 34, F₂, 4) (dual of [34, 24, 5]-code), but
- â€œBoVâ€ bound on codes from Brouwerâ€™s database [i]
linear OA(2⁴⁷, 58, F₂, 24) (dual of [58, 11, 25]-code), but
- discarding factors / shortening the dual code would yield linear OA(2⁴⁷, 54, F₂, 24) (dual of [54, 7, 25]-code), but
  - adding a parity check bit [i] would yield linear OA(2⁴⁸, 55, F₂, 25) (dual of [55, 7, 26]-code), but
    - â€œvT4â€ bound on codes from Brouwerâ€™s database [i]

Mode: Bound (linear).

None.

The following results depend on this result:

	Result		Method
1	No linear OA(2¹², 59, F₂, 5) (dual of [59, 47, 6]-code)	[i]	Truncation
2	No linear OOA(2¹², 58, F₂, 2, 5) (dual of [(58, 2), 104, 6]-NRT-code)	[i]	m-Reduction for OOAs
3	No linear OOA(2¹¹, 58, F₂, 2, 4) (dual of [(58, 2), 105, 5]-NRT-code)	[i]	Depth Reduction
4	No linear OOA(2¹¹, 58, F₂, 3, 4) (dual of [(58, 3), 163, 5]-NRT-code)	[i]
5	No linear OOA(2¹¹, 58, F₂, 4, 4) (dual of [(58, 4), 221, 5]-NRT-code)	[i]
6	No linear OOA(2¹¹, 58, F₂, 5, 4) (dual of [(58, 5), 279, 5]-NRT-code)	[i]
7	No linear OOA(2¹¹, 58, F₂, 6, 4) (dual of [(58, 6), 337, 5]-NRT-code)	[i]
8	No linear OOA(2¹¹, 58, F₂, 7, 4) (dual of [(58, 7), 395, 5]-NRT-code)	[i]
9	No linear OOA(2¹¹, 58, F₂, 8, 4) (dual of [(58, 8), 453, 5]-NRT-code)	[i]
10	No digital (7, 11, 58)-net over F₂	[i]	Extracting Embedded Orthogonal Array
11	No linear OA(2⁴⁹, 60, F₂, 24) (dual of [60, 11, 25]-code)	[i]	ConstructionÂ Y1 (Bound)