MinT - Information on Result #570708

Information on Result #570708

There is no linear OOA(3¹⁹⁷, 203, F₃, 3, 133) (dual of [(203, 3), 412, 134]-NRT-code), because 1 times depth reduction would yield linear OOA(3¹⁹⁷, 203, F₃, 2, 133) (dual of [(203, 2), 209, 134]-NRT-code), but

4 step m-reduction [i] would yield linear OA(3¹⁹³, 203, F₃, 129) (dual of [203, 10, 130]-code), but
- constructionÂ Y1 [i] would yield
  1. linear OA(3¹⁹², 199, F₃, 129) (dual of [199, 7, 130]-code), but
    - residual code [i] would yield linear OA(3⁶³, 69, F₃, 43) (dual of [69, 6, 44]-code), but
      - â€œMaâ€ bound on codes from Brouwerâ€™s database [i]
  2. OA(3¹⁰, 203, S₃, 4), but
    - discarding factors would yield OA(3¹⁰, 172, S₃, 4), but
      - the Rao or (dual) Hamming bound shows that MÂ â‰¥ 59169 > 3¹⁰ [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

None.