MinT - Information on Result #553324

Information on Result #553324

There is no linear OOA(2¹⁹², 182, F₂, 2, 107) (dual of [(182, 2), 172, 108]-NRT-code), because 19 step m-reduction would yield linear OA(2¹⁷³, 182, F₂, 88) (dual of [182, 9, 89]-code), but

residual code [i] would yield linear OA(2⁸⁵, 93, F₂, 44) (dual of [93, 8, 45]-code), but
- residual code [i] would yield linear OA(2⁴¹, 48, F₂, 22) (dual of [48, 7, 23]-code), but
  - residual code [i] 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.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		Method
1	No linear OOA(2¹⁹², 182, F₂, 3, 107) (dual of [(182, 3), 354, 108]-NRT-code)	[i]	Depth Reduction
2	No linear OOA(2¹⁹², 182, F₂, 4, 107) (dual of [(182, 4), 536, 108]-NRT-code)	[i]
3	No linear OOA(2¹⁹², 182, F₂, 5, 107) (dual of [(182, 5), 718, 108]-NRT-code)	[i]