MinT - Information on Result #553475

Information on Result #553475

There is no linear OOA(2¹⁹⁷, 209, F₂, 2, 99) (dual of [(209, 2), 221, 100]-NRT-code), because 1 step m-reduction would yield linear OA(2¹⁹⁶, 209, F₂, 98) (dual of [209, 13, 99]-code), but

constructionÂ Y1 [i] would yield
1. linear OA(2¹⁹⁵, 205, F₂, 98) (dual of [205, 10, 99]-code), but
  - residual code [i] would yield linear OA(2⁹⁷, 106, F₂, 49) (dual of [106, 9, 50]-code), but
    - 1 times truncation [i] would yield linear OA(2⁹⁶, 105, F₂, 48) (dual of [105, 9, 49]-code), but
      - residual code [i] would yield linear OA(2⁴⁸, 56, F₂, 24) (dual of [56, 8, 25]-code), but
        adding a parity check bit [i] would yield linear OA(2⁴⁹, 57, F₂, 25) (dual of [57, 8, 26]-code), but
        â€œBJVâ€ bound on codes from Brouwerâ€™s database [i]
2. OA(2¹³, 209, S₂, 4), but
  - discarding factors would yield OA(2¹³, 128, S₂, 4), but
    - the Rao or (dual) Hamming bound shows that MÂ â‰¥ 8257 > 2¹³ [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(2¹⁹⁷, 209, F₂, 3, 99) (dual of [(209, 3), 430, 100]-NRT-code)	[i]	Depth Reduction
2	No linear OOA(2¹⁹⁷, 209, F₂, 4, 99) (dual of [(209, 4), 639, 100]-NRT-code)	[i]
3	No linear OOA(2¹⁹⁷, 209, F₂, 5, 99) (dual of [(209, 5), 848, 100]-NRT-code)	[i]
4	No linear OOA(2¹⁹⁷, 209, F₂, 6, 99) (dual of [(209, 6), 1057, 100]-NRT-code)	[i]
5	No linear OOA(2¹⁹⁷, 209, F₂, 7, 99) (dual of [(209, 7), 1266, 100]-NRT-code)	[i]
6	No linear OOA(2¹⁹⁷, 209, F₂, 8, 99) (dual of [(209, 8), 1475, 100]-NRT-code)	[i]