MinT - Information on Result #562755

Information on Result #562755

There is no linear OOA(7¹⁵, 30, F₇, 2, 13) (dual of [(30, 2), 45, 14]-NRT-code), because 1 step m-reduction would yield linear OA(7¹⁴, 30, F₇, 12) (dual of [30, 16, 13]-code), but

constructionÂ Y1 [i] would yield
1. linear OA(7¹³, 16, F₇, 12) (dual of [16, 3, 13]-code), but
  - bound for almost-MDS-codes with dimension nÂ =Â 3 [i]
2. linear OA(7¹⁶, 30, F₇, 14) (dual of [30, 14, 15]-code), but
  - discarding factors / shortening the dual code would yield linear OA(7¹⁶, 24, F₇, 14) (dual of [24, 8, 15]-code), but
    - residual code [i] would yield OA(7², 9, S₇, 2), but
      - bound for OAs with strength kÂ =Â 2 [i]
      - the Rao or (dual) Hamming bound shows that MÂ â‰¥ 55 > 7² [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(7¹⁵, 30, F₇, 3, 13) (dual of [(30, 3), 75, 14]-NRT-code)	[i]		Depth Reduction