MinT - Information on Result #547734

Information on Result #547734

There is no linear OA(3¹⁸, 31, F₃, 12) (dual of [31, 13, 13]-code), because constructionÂ Y1 would yield

linear OA(3¹⁷, 22, F₃, 12) (dual of [22, 5, 13]-code), but
- constructionÂ Y1 [i] would yield
  1. linear OA(3¹⁶, 19, F₃, 12) (dual of [19, 3, 13]-code), but
    - Griesmer bound [i]
  2. linear OA(3⁵, 22, F₃, 3) (dual of [22, 17, 4]-code or 22-cap in PG(4,3)), but
    - discarding factors / shortening the dual code would yield linear OA(3⁵, 21, F₃, 3) (dual of [21, 16, 4]-code or 21-cap in PG(4,3)), but
      - 20 is the largest size of a cap in PG(4,Â 3) [i]
OA(3¹³, 31, S₃, 9), but
- the linear programming bound shows that MÂ â‰¥ 223 826947 806735 / 135 356861 > 3¹³ [i]

Mode: Bound (linear).

None.

None.