MinT - Information on Result #555176

Information on Result #555176

There is no linear OOA(2²⁵⁸, 270, F₂, 2, 129) (dual of [(270, 2), 282, 130]-NRT-code), because 1 step m-reduction would yield linear OA(2²⁵⁷, 270, F₂, 128) (dual of [270, 13, 129]-code), but

constructionÂ Y1 [i] would yield
1. linear OA(2²⁵⁶, 266, F₂, 128) (dual of [266, 10, 129]-code), but
  - residual code [i] would yield linear OA(2¹²⁸, 137, F₂, 64) (dual of [137, 9, 65]-code), but
    - residual code [i] would yield linear OA(2⁶⁴, 72, F₂, 32) (dual of [72, 8, 33]-code), but
      - adding a parity check bit [i] would yield linear OA(2⁶⁵, 73, F₂, 33) (dual of [73, 8, 34]-code), but
        â€œBJVâ€ bound on codes from Brouwerâ€™s database [i]
2. OA(2¹³, 270, S₂, 4), but
  - discarding factors would yield OA(2¹³, 128, S₂, 4), but
    - the Rao or (dual) Hamming bound shows that MÂ â‰¥ 8257 > 2¹³ [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(2²⁵⁸, 270, F₂, 3, 129) (dual of [(270, 3), 552, 130]-NRT-code)	[i]	Depth Reduction
2	No linear OOA(2²⁵⁸, 270, F₂, 4, 129) (dual of [(270, 4), 822, 130]-NRT-code)	[i]
3	No linear OOA(2²⁵⁸, 270, F₂, 5, 129) (dual of [(270, 5), 1092, 130]-NRT-code)	[i]
4	No linear OOA(2²⁵⁸, 270, F₂, 6, 129) (dual of [(270, 6), 1362, 130]-NRT-code)	[i]
5	No linear OOA(2²⁵⁸, 270, F₂, 7, 129) (dual of [(270, 7), 1632, 130]-NRT-code)	[i]
6	No linear OOA(2²⁵⁸, 270, F₂, 8, 129) (dual of [(270, 8), 1902, 130]-NRT-code)	[i]