MinT - Information on Result #548547

Information on Result #548547

There is no linear OA(2¹⁵⁸, 244, F₂, 74) (dual of [244, 86, 75]-code), because constructionÂ Y1 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]
linear OA(2⁸⁶, 244, F₂, 34) (dual of [244, 158, 35]-code), but
- discarding factors / shortening the dual code would yield linear OA(2⁸⁶, 239, F₂, 34) (dual of [239, 153, 35]-code), but
  - the Johnson bound shows that NÂ â‰¤ 11164 899023 828415 148240 405183 101489 722460 406426 < 2¹⁵³ [i]

Mode: Bound (linear).

None.

The following results depend on this result:

	Result		This result only	Method
1	No linear OA(2¹⁵⁹, 245, F₂, 75) (dual of [245, 86, 76]-code)	[i]		Truncation
2	No linear OOA(2¹⁵⁹, 244, F₂, 2, 75) (dual of [(244, 2), 329, 76]-NRT-code)	[i]		m-Reduction for OOAs