MinT - Information on Result #547777

Information on Result #547777

There is no linear OA(3¹³¹, 228, F₃, 83) (dual of [228, 97, 84]-code), because constructionÂ Y1 would yield

linear OA(3¹³⁰, 169, F₃, 83) (dual of [169, 39, 84]-code), but
- constructionÂ Y1 [i] would yield
  1. OA(3¹²⁹, 149, S₃, 83), but
    - the linear programming bound shows that MÂ â‰¥ 84 319128 221217 735495 636798 406504 571731 768077 225953 505729 024301 422296 511468 / 1 784703 172945 > 3¹²⁹ [i]
  2. OA(3³⁹, 169, S₃, 20), but
    - the Rao or (dual) Hamming bound shows that MÂ â‰¥ 4 219632 770903 631459 > 3³⁹ [i]
linear OA(3⁹⁷, 228, F₃, 59) (dual of [228, 131, 60]-code), but
- discarding factors / shortening the dual code would yield linear OA(3⁹⁷, 225, F₃, 59) (dual of [225, 128, 60]-code), but
  - constructionÂ Y1 [i] would yield
    1. OA(3⁹⁶, 144, S₃, 59), but
      - the linear programming bound shows that MÂ â‰¥ 2236 401438 247250 718182 900374 183456 399210 453427 110900 255699 874712 354347 141530 819695 / 326304 173287 366006 276464 537104 634223 > 3⁹⁶ [i]
    2. linear OA(3¹²⁸, 225, F₃, 81) (dual of [225, 97, 82]-code), but
      - discarding factors / shortening the dual code would yield linear OA(3¹²⁸, 214, F₃, 81) (dual of [214, 86, 82]-code), but
        residual code [i] would yield OA(3⁴⁷, 132, S₃, 27), but
        the linear programming bound shows that MÂ â‰¥ 101 853735 825646 993501 712845 933577 029990 584494 296875 / 3711 656810 327991 475017 244489 > 3⁴⁷ [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.