Information on Result #1297951

Linear OA(351, 531469, F3, 6) (dual of [531469, 531418, 7]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(350, 531467, F3, 6) (dual of [531467, 531417, 7]-code), using
    • construction X4 applied to Ce(6) ⊂ Ce(3) [i] based on
      1. linear OA(349, 531441, F3, 7) (dual of [531441, 531392, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
      2. linear OA(325, 531441, F3, 4) (dual of [531441, 531416, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
      3. linear OA(325, 26, F3, 25) (dual of [26, 1, 26]-code or 26-arc in PG(24,3)), using
      4. linear OA(31, 26, F3, 1) (dual of [26, 25, 2]-code), using
  2. linear OA(350, 531468, F3, 5) (dual of [531468, 531418, 6]-code), using Gilbert–VarÅ¡amov bound and bm = 350 > Vbs−1(k−1) = 53187 635733 407401 626299 [i]
  3. linear OA(30, 1, F3, 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(351, 531469, F3, 2, 6) (dual of [(531469, 2), 1062887, 7]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(351, 531469, F3, 3, 6) (dual of [(531469, 3), 1594356, 7]-NRT-code) [i]
3Linear OOA(351, 531469, F3, 4, 6) (dual of [(531469, 4), 2125825, 7]-NRT-code) [i]
4Linear OOA(351, 531469, F3, 5, 6) (dual of [(531469, 5), 2657294, 7]-NRT-code) [i]