MinT - Information on Result #550839

Information on Result #550839

There is no linear OOA(2⁶⁷, 71, F₂, 2, 36) (dual of [(71, 2), 75, 37]-NRT-code), because 4 step m-reduction 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 OOA(2⁶⁷, 71, F₂, 3, 36) (dual of [(71, 3), 146, 37]-NRT-code)	[i]		Depth Reduction
2	No linear OOA(2⁶⁷, 71, F₂, 4, 36) (dual of [(71, 4), 217, 37]-NRT-code)	[i]
3	No linear OOA(2⁶⁷, 71, F₂, 5, 36) (dual of [(71, 5), 288, 37]-NRT-code)	[i]
4	No linear OOA(2⁶⁷, 71, F₂, 6, 36) (dual of [(71, 6), 359, 37]-NRT-code)	[i]
5	No linear OOA(2⁶⁷, 71, F₂, 7, 36) (dual of [(71, 7), 430, 37]-NRT-code)	[i]
6	No linear OOA(2⁶⁷, 71, F₂, 8, 36) (dual of [(71, 8), 501, 37]-NRT-code)	[i]