MinT - Information on Result #555107

Information on Result #555107

There is no linear OOA(2²⁵⁶, 288, F₂, 2, 125) (dual of [(288, 2), 320, 126]-NRT-code), because 1 step m-reduction would yield linear OA(2²⁵⁵, 288, F₂, 124) (dual of [288, 33, 125]-code), but

constructionÂ Y1 [i] would yield
1. linear OA(2²⁵⁴, 278, F₂, 124) (dual of [278, 24, 125]-code), but
  - residual code [i] would yield linear OA(2¹³⁰, 153, F₂, 62) (dual of [153, 23, 63]-code), but
    - adding a parity check bit [i] would yield linear OA(2¹³¹, 154, F₂, 63) (dual of [154, 23, 64]-code), but
      - â€œBKâ€ bound on codes from Brouwerâ€™s database [i]
2. OA(2³³, 288, S₂, 10), but
  - discarding factors would yield OA(2³³, 254, S₂, 10), but
    - the Rao or (dual) Hamming bound shows that MÂ â‰¥ 8640 218941 > 2³³ [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(2²⁵⁶, 288, F₂, 3, 125) (dual of [(288, 3), 608, 126]-NRT-code)	[i]	Depth Reduction
2	No linear OOA(2²⁵⁶, 288, F₂, 4, 125) (dual of [(288, 4), 896, 126]-NRT-code)	[i]
3	No linear OOA(2²⁵⁶, 288, F₂, 5, 125) (dual of [(288, 5), 1184, 126]-NRT-code)	[i]
4	No linear OOA(2²⁵⁶, 288, F₂, 6, 125) (dual of [(288, 6), 1472, 126]-NRT-code)	[i]
5	No linear OOA(2²⁵⁶, 288, F₂, 7, 125) (dual of [(288, 7), 1760, 126]-NRT-code)	[i]
6	No linear OOA(2²⁵⁶, 288, F₂, 8, 125) (dual of [(288, 8), 2048, 126]-NRT-code)	[i]