MinT - Information on Result #573616

Information on Result #573616

There is no linear OOA(4¹⁶⁸, 188, F₄, 3, 126) (dual of [(188, 3), 396, 127]-NRT-code), because 1 times depth reduction would yield linear OOA(4¹⁶⁸, 188, F₄, 2, 126) (dual of [(188, 2), 208, 127]-NRT-code), but

2 step m-reduction [i] would yield linear OA(4¹⁶⁶, 188, F₄, 124) (dual of [188, 22, 125]-code), but
- constructionÂ Y1 [i] would yield
  1. linear OA(4¹⁶⁵, 176, F₄, 124) (dual of [176, 11, 125]-code), but
    - residual code [i] would yield linear OA(4⁴¹, 51, F₄, 31) (dual of [51, 10, 32]-code), but
      - â€œGurâ€ bound on codes from Brouwerâ€™s database [i]
  2. OA(4²², 188, S₄, 12), but
    - discarding factors would yield OA(4²², 164, S₄, 12), but
      - the Rao or (dual) Hamming bound shows that MÂ â‰¥ 18 187369 733464 > 4²² [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.