MinT - Information on Result #555351

Information on Result #555351

There is no linear OOA(3⁴³, 53, F₃, 2, 29) (dual of [(53, 2), 63, 30]-NRT-code), because 1 step m-reduction would yield linear OA(3⁴², 53, F₃, 28) (dual of [53, 11, 29]-code), but

constructionÂ Y1 [i] would yield
1. linear OA(3⁴¹, 47, F₃, 28) (dual of [47, 6, 29]-code), but
  - â€œHJâ€ bound on codes from Brouwerâ€™s database [i]
2. OA(3¹¹, 53, S₃, 6), but
  - discarding factors would yield OA(3¹¹, 52, S₃, 6), but
    - the Rao or (dual) Hamming bound shows that MÂ â‰¥ 182209 > 3¹¹ [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(3⁴³, 53, F₃, 3, 29) (dual of [(53, 3), 116, 30]-NRT-code)	[i]	Depth Reduction
2	No linear OOA(3⁴³, 53, F₃, 4, 29) (dual of [(53, 4), 169, 30]-NRT-code)	[i]
3	No linear OOA(3⁴³, 53, F₃, 5, 29) (dual of [(53, 5), 222, 30]-NRT-code)	[i]