MinT - Information on Result #546554

Information on Result #546554

There is no linear OA(2²⁵⁵, 265, F₂, 128) (dual of [265, 10, 129]-code), because residual code would yield linear OA(2¹²⁷, 136, F₂, 64) (dual of [136, 9, 65]-code), but

residual code [i] would yield linear OA(2⁶³, 71, F₂, 32) (dual of [71, 8, 33]-code), but
- residual code [i] would yield linear OA(2³¹, 38, F₂, 16) (dual of [38, 7, 17]-code), but
  - residual code [i] would yield linear OA(2¹⁵, 21, F₂, 8) (dual of [21, 6, 9]-code), but
    - residual code [i] would yield linear OA(2⁷, 12, F₂, 4) (dual of [12, 5, 5]-code), but
      - bound by Fontaine and Peterson [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		This result only	Method
1	No linear OA(2²⁵⁶, 266, F₂, 129) (dual of [266, 10, 130]-code)	[i]		Truncation
2	No linear OOA(2²⁵⁶, 265, F₂, 2, 129) (dual of [(265, 2), 274, 130]-NRT-code)	[i]		m-Reduction for OOAs
3	No linear OOA(2²⁵⁸, 265, F₂, 2, 131) (dual of [(265, 2), 272, 132]-NRT-code)	[i]
4	No linear OOA(2²⁵⁹, 265, F₂, 2, 132) (dual of [(265, 2), 271, 133]-NRT-code)	[i]
5	No linear OOA(2²⁶⁰, 265, F₂, 2, 133) (dual of [(265, 2), 270, 134]-NRT-code)	[i]
6	No linear OOA(2²⁵⁵, 265, F₂, 2, 128) (dual of [(265, 2), 275, 129]-NRT-code)	[i]		Depth Reduction
7	No linear OOA(2²⁵⁵, 265, F₂, 3, 128) (dual of [(265, 3), 540, 129]-NRT-code)	[i]
8	No linear OOA(2²⁵⁵, 265, F₂, 4, 128) (dual of [(265, 4), 805, 129]-NRT-code)	[i]
9	No linear OOA(2²⁵⁵, 265, F₂, 5, 128) (dual of [(265, 5), 1070, 129]-NRT-code)	[i]
10	No linear OOA(2²⁵⁵, 265, F₂, 6, 128) (dual of [(265, 6), 1335, 129]-NRT-code)	[i]
11	No linear OOA(2²⁵⁵, 265, F₂, 7, 128) (dual of [(265, 7), 1600, 129]-NRT-code)	[i]
12	No linear OOA(2²⁵⁵, 265, F₂, 8, 128) (dual of [(265, 8), 1865, 129]-NRT-code)	[i]
13	No digital (127, 255, 265)-net over F₂	[i]		Extracting Embedded Orthogonal Array