MinT - Information on Result #550639

Information on Result #550639

There is no linear OOA(2³⁹, 45, F₂, 2, 21) (dual of [(45, 2), 51, 22]-NRT-code), because 1 step m-reduction would yield linear OA(2³⁸, 45, F₂, 20) (dual of [45, 7, 21]-code), but

residual code [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.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	No linear OOA(2³⁹, 45, F₂, 3, 21) (dual of [(45, 3), 96, 22]-NRT-code)	[i]		Depth Reduction
2	No linear OOA(2³⁹, 45, F₂, 4, 21) (dual of [(45, 4), 141, 22]-NRT-code)	[i]
3	No linear OOA(2³⁹, 45, F₂, 5, 21) (dual of [(45, 5), 186, 22]-NRT-code)	[i]
4	No linear OOA(2³⁹, 45, F₂, 6, 21) (dual of [(45, 6), 231, 22]-NRT-code)	[i]
5	No linear OOA(2³⁹, 45, F₂, 7, 21) (dual of [(45, 7), 276, 22]-NRT-code)	[i]
6	No linear OOA(2³⁹, 45, F₂, 8, 21) (dual of [(45, 8), 321, 22]-NRT-code)	[i]