MinT - Information on Result #559127

Information on Result #559127

There is no linear OOA(4⁴⁴, 55, F₄, 2, 33) (dual of [(55, 2), 66, 34]-NRT-code), because 1 step m-reduction would yield linear OA(4⁴³, 55, F₄, 32) (dual of [55, 12, 33]-code), but

constructionÂ Y1 [i] would yield
1. linear OA(4⁴², 47, F₄, 32) (dual of [47, 5, 33]-code), but
  - constructionÂ Y1 [i] would yield
    1. linear OA(4⁴¹, 44, F₄, 32) (dual of [44, 3, 33]-code), but
      - Griesmer bound [i]
    2. linear OA(4⁵, 47, F₄, 3) (dual of [47, 42, 4]-code or 47-cap in PG(4,4)), but
      - discarding factors / shortening the dual code would yield linear OA(4⁵, 42, F₄, 3) (dual of [42, 37, 4]-code or 42-cap in PG(4,4)), but
        41 is the largest size of a cap in PG(4,Â 4) [i]
2. OA(4¹², 55, S₄, 8), but
  - discarding factors would yield OA(4¹², 49, S₄, 8), but
    - the Rao or (dual) Hamming bound shows that MÂ â‰¥ 17 670136 > 4¹² [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		This result only	Method
1	No linear OOA(4⁴⁴, 55, F₄, 3, 33) (dual of [(55, 3), 121, 34]-NRT-code)	[i]		Depth Reduction