MinT - Information on Result #546165

Information on Result #546165

There is no linear OA(2⁴¹, 48, F₂, 22) (dual of [48, 7, 23]-code), because residual code would yield linear OA(2¹⁹, 25, F₂, 11) (dual of [25, 6, 12]-code), but

1 times truncation [i] would yield linear OA(2¹⁸, 24, F₂, 10) (dual of [24, 6, 11]-code), but
- residual code [i] would yield linear OA(2⁸, 13, F₂, 5) (dual of [13, 5, 6]-code), but
  - 1 times truncation [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.

Compare with Markus Grassl’s online database of code parameters.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	No linear OA(2⁴², 49, F₂, 23) (dual of [49, 7, 24]-code)	[i]		Truncation
2	No linear OOA(2⁴¹, 48, F₂, 2, 22) (dual of [(48, 2), 55, 23]-NRT-code)	[i]		Depth Reduction
3	No linear OOA(2⁴¹, 48, F₂, 3, 22) (dual of [(48, 3), 103, 23]-NRT-code)	[i]
4	No linear OOA(2⁴¹, 48, F₂, 4, 22) (dual of [(48, 4), 151, 23]-NRT-code)	[i]
5	No linear OOA(2⁴¹, 48, F₂, 5, 22) (dual of [(48, 5), 199, 23]-NRT-code)	[i]
6	No linear OOA(2⁴¹, 48, F₂, 6, 22) (dual of [(48, 6), 247, 23]-NRT-code)	[i]
7	No linear OOA(2⁴¹, 48, F₂, 7, 22) (dual of [(48, 7), 295, 23]-NRT-code)	[i]
8	No linear OOA(2⁴¹, 48, F₂, 8, 22) (dual of [(48, 8), 343, 23]-NRT-code)	[i]
9	No linear OA(2⁸⁵, 93, F₂, 44) (dual of [93, 8, 45]-code)	[i]		Residual Code