MinT - Information on Result #547744

Information on Result #547744

There is no linear OA(3⁵⁴, 65, F₃, 36) (dual of [65, 11, 37]-code), because constructionÂ Y1 would yield

linear OA(3⁵³, 59, F₃, 36) (dual of [59, 6, 37]-code), but
- constructionÂ Y1 [i] would yield
  1. linear OA(3⁵², 56, F₃, 36) (dual of [56, 4, 37]-code), but
    - Griesmer bound [i]
  2. linear OA(3⁶, 59, F₃, 3) (dual of [59, 53, 4]-code or 59-cap in PG(5,3)), but
    - discarding factors / shortening the dual code would yield linear OA(3⁶, 57, F₃, 3) (dual of [57, 51, 4]-code or 57-cap in PG(5,3)), but
      - doubling the cap [i] would yield 114-cap in AG(6,3), but
        discarding factors / shortening the dual code would yield 113-cap in AG(6,3), but
        bound on the size of affine caps [i]
OA(3¹¹, 65, S₃, 6), but
- discarding factors would yield OA(3¹¹, 52, S₃, 6), but
  - the Rao or (dual) Hamming bound shows that MÂ â‰¥ 182209 > 3¹¹ [i]

Mode: Bound (linear).

None.

None.