MinT - Information on Result #2169190

Information on Result #2169190

There is no linear OA(7¹⁵, 31, F₇, 13) (dual of [31, 16, 14]-code), because 1 times truncation 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.

Compare with Markus Grassl’s online database of code parameters.

Other Results with Identical Parameters

None.

Depending Results

None.