MinT - Information on Result #548649

Information on Result #548649

There is no linear OA(9¹³, 53, F₉, 11) (dual of [53, 40, 12]-code), because constructionÂ Y1 would yield

linear OA(9¹², 17, F₉, 11) (dual of [17, 5, 12]-code), but
- â€œMPaâ€ bound on codes from Brouwerâ€™s database [i]
linear OA(9⁴⁰, 53, F₉, 36) (dual of [53, 13, 37]-code), but
- discarding factors / shortening the dual code would yield linear OA(9⁴⁰, 48, F₉, 36) (dual of [48, 8, 37]-code), but
  - residual code [i] would yield linear OA(9⁴, 11, F₉, 4) (dual of [11, 7, 5]-code or 11-arc in PG(3,9)), but
    - bound for MDS codes [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 OOA(9¹³, 53, F₉, 2, 11) (dual of [(53, 2), 93, 12]-NRT-code)	[i]		Depth Reduction
2	No linear OOA(9¹³, 53, F₉, 3, 11) (dual of [(53, 3), 146, 12]-NRT-code)	[i]		Depth Reduction
3	No digital (2, 13, 53)-net over F₉	[i]		Extracting Embedded Orthogonal Array
4	No linear OA(9⁴⁷, 60, F₉, 42) (dual of [60, 13, 43]-code)	[i]		ConstructionÂ Y1 (Bound)