MinT - Information on Result #2171195

Information on Result #2171195

There is no linear OA(9⁴³, 48, F₉, 39) (dual of [48, 5, 40]-code), because 3 times truncation would yield linear OA(9⁴⁰, 45, F₉, 36) (dual of [45, 5, 37]-code), but

constructionÂ Y1 [i] would yield
1. OA(9³⁹, 41, S₉, 36), but
  - the (dual) Plotkin bound shows that MÂ â‰¥ 739 044147 071729 616580 416051 031916 488005 / 37 > 9³⁹ [i]
2. OA(9⁵, 45, S₉, 4), but
  - discarding factors would yield OA(9⁵, 44, S₉, 4), but
    - the Rao or (dual) Hamming bound shows that MÂ â‰¥ 60897 > 9⁵ [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.

Compare with Markus Grassl’s online database of code parameters.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	No linear OA(9⁴⁴, 80, F₉, 39) (dual of [80, 36, 40]-code)	[i]		ConstructionÂ Y1 (Bound)