MinT - Information on Result #526560

Information on Result #526560

There is no linear OA(4¹⁰, 31795, F₄, 3) (dual of [31795, 31785, 4]-code or 31795-cap in PG(9,4)), because removing affine subspaces would yield

linear OA(4⁷, 632, F₄, 3) (dual of [632, 625, 4]-code or 632-cap in PG(6,4)), but
- 2 times Hill recurrence [i] would yield linear OA(4⁵, 42, F₄, 3) (dual of [42, 37, 4]-code or 42-cap in PG(4,4)), but
  - 41 is the largest size of a cap in PG(4,Â 4) [i]
1752-cap in AG(7,4), but
- 3 times the recursive bound from Bierbrauer and Edel [i] would yield 41-cap in AG(4,4), but
  - bound on the size of affine caps [i]
6329-cap in AG(8,4), but
- 4 times the recursive bound from Bierbrauer and Edel [i] would yield 41-cap in AG(4,4) (see above)
23085-cap in AG(9,4), but
- 5 times the recursive bound from Bierbrauer and Edel [i] would yield 41-cap in AG(4,4) (see above)

Mode: Bound (linear).

None.

None.