Information on Result #1301333

Linear OA(551, 15641, F5, 10) (dual of [15641, 15590, 11]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(550, 15639, F5, 10) (dual of [15639, 15589, 11]-code), using
    • construction X4 applied to Ce(10) ⊂ Ce(7) [i] based on
      1. linear OA(549, 15625, F5, 11) (dual of [15625, 15576, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
      2. linear OA(537, 15625, F5, 8) (dual of [15625, 15588, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
      3. linear OA(513, 14, F5, 13) (dual of [14, 1, 14]-code or 14-arc in PG(12,5)), using
      4. linear OA(51, 14, F5, 1) (dual of [14, 13, 2]-code), using
  2. linear OA(550, 15640, F5, 9) (dual of [15640, 15590, 10]-code), using Gilbert–VarÅ¡amov bound and bm = 550 > Vbs−1(k−1) = 5806 429114 305176 921704 526252 028397 [i]
  3. linear OA(50, 1, F5, 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(551, 15641, F5, 2, 10) (dual of [(15641, 2), 31231, 11]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(551, 15641, F5, 3, 10) (dual of [(15641, 3), 46872, 11]-NRT-code) [i]
3Digital (41, 51, 15641)-net over F5 [i]