MinT - Information on Result #552336

Information on Result #552336

There is no linear OOA(2¹⁵⁸, 210, F₂, 2, 75) (dual of [(210, 2), 262, 76]-NRT-code), because 1 step m-reduction would yield linear OA(2¹⁵⁷, 210, F₂, 74) (dual of [210, 53, 75]-code), but

constructionÂ Y1 [i] would yield
1. 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]
2. OA(2⁵³, 210, S₂, 20), but
  - discarding factors would yield OA(2⁵³, 182, S₂, 20), but
    - the Rao or (dual) Hamming bound shows that MÂ â‰¥ 9064 436853 738748 > 2⁵³ [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(2¹⁵⁸, 210, F₂, 3, 75) (dual of [(210, 3), 472, 76]-NRT-code)	[i]	Depth Reduction
2	No linear OOA(2¹⁵⁸, 210, F₂, 4, 75) (dual of [(210, 4), 682, 76]-NRT-code)	[i]
3	No linear OOA(2¹⁵⁸, 210, F₂, 5, 75) (dual of [(210, 5), 892, 76]-NRT-code)	[i]
4	No linear OOA(2¹⁵⁸, 210, F₂, 6, 75) (dual of [(210, 6), 1102, 76]-NRT-code)	[i]
5	No linear OOA(2¹⁵⁸, 210, F₂, 7, 75) (dual of [(210, 7), 1312, 76]-NRT-code)	[i]
6	No linear OOA(2¹⁵⁸, 210, F₂, 8, 75) (dual of [(210, 8), 1522, 76]-NRT-code)	[i]