Information on Result #1301288

Linear OA(539, 15641, F5, 8) (dual of [15641, 15602, 9]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(538, 15639, F5, 8) (dual of [15639, 15601, 9]-code), using
    • construction X4 applied to Ce(7) ⊂ Ce(5) [i] based on
      1. 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]
      2. linear OA(525, 15625, F5, 6) (dual of [15625, 15600, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [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(538, 15640, F5, 7) (dual of [15640, 15602, 8]-code), using Gilbert–VarÅ¡amov bound and bm = 538 > Vbs−1(k−1) = 83 158452 840508 053832 593901 [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(539, 15641, F5, 2, 8) (dual of [(15641, 2), 31243, 9]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(539, 15641, F5, 3, 8) (dual of [(15641, 3), 46884, 9]-NRT-code) [i]
3Digital (31, 39, 15641)-net over F5 [i]