Information on Result #572536
There is no linear OOA(413, 1599334, F4, 3, 3) (dual of [(1599334, 3), 4797989, 4]-NRT-code), because 2 times depth reduction would yield linear OA(413, 1599334, F4, 3) (dual of [1599334, 1599321, 4]-code or 1599334-cap in PG(12,4)), but
- removing affine subspaces [i] would yield
- linear OA(47, 608, F4, 3) (dual of [608, 601, 4]-code or 608-cap in PG(6,4)), but
- 1 times Hill recurrence [i] would yield linear OA(46, 154, F4, 3) (dual of [154, 148, 4]-code or 154-cap in PG(5,4)), but
- construction Y1 [i] would yield
- linear OA(45, 42, F4, 3) (dual of [42, 37, 4]-code or 42-cap in PG(4,4)), but
- linear OA(4148, 154, F4, 112) (dual of [154, 6, 113]-code), but
- discarding factors / shortening the dual code would yield linear OA(4148, 153, F4, 112) (dual of [153, 5, 113]-code), but
- residual code [i] would yield linear OA(436, 40, F4, 28) (dual of [40, 4, 29]-code), but
- residual code [i] would yield linear OA(48, 11, F4, 7) (dual of [11, 3, 8]-code), but
- residual code [i] would yield linear OA(436, 40, F4, 28) (dual of [40, 4, 29]-code), but
- discarding factors / shortening the dual code would yield linear OA(4148, 153, F4, 112) (dual of [153, 5, 113]-code), but
- construction Y1 [i] would yield
- 1 times Hill recurrence [i] would yield linear OA(46, 154, F4, 3) (dual of [154, 148, 4]-code or 154-cap in PG(5,4)), but
- 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
- 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)
- 84865-cap in AG(10,4), but
- 6 times the recursive bound from Bierbrauer and Edel [i] would yield 41-cap in AG(4,4) (see above)
- 314041-cap in AG(11,4), but
- 7 times the recursive bound from Bierbrauer and Edel [i] would yield 41-cap in AG(4,4) (see above)
- 1168660-cap in AG(12,4), but
- 8 times the recursive bound from Bierbrauer and Edel [i] would yield 41-cap in AG(4,4) (see above)
- linear OA(47, 608, F4, 3) (dual of [608, 601, 4]-code or 608-cap in PG(6,4)), but
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.
Other Results with Identical Parameters
None.
Depending Results
None.