Information on Result #1299897

Linear OA(469, 4194330, F4, 8) (dual of [4194330, 4194261, 9]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(468, 4194328, F4, 8) (dual of [4194328, 4194260, 9]-code), using
    • construction X4 applied to Ce(8) ⊂ Ce(5) [i] based on
      1. linear OA(467, 4194304, F4, 9) (dual of [4194304, 4194237, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
      2. linear OA(445, 4194304, F4, 6) (dual of [4194304, 4194259, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
      3. linear OA(423, 24, F4, 23) (dual of [24, 1, 24]-code or 24-arc in PG(22,4)), using
      4. linear OA(41, 24, F4, 1) (dual of [24, 23, 2]-code), using
  2. linear OA(468, 4194329, F4, 7) (dual of [4194329, 4194261, 8]-code), using Gilbert–VarÅ¡amov bound and bm = 468 > Vbs−1(k−1) = 5512 746519 677817 912237 124646 478493 830739 [i]
  3. linear OA(40, 1, F4, 0) (dual of [1, 1, 1]-code), using

Mode: 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

The following results depend on this result:

ResultThis
result
only		Method
1Linear OOA(469, 4194330, F4, 2, 8) (dual of [(4194330, 2), 8388591, 9]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(469, 4194330, F4, 3, 8) (dual of [(4194330, 3), 12582921, 9]-NRT-code) [i]
3Digital (61, 69, 4194330)-net over F4 [i]
4Linear OOA(469, 2097165, F4, 2, 8) (dual of [(2097165, 2), 4194261, 9]-NRT-code) [i]OOA Folding