Information on Result #1301292

Linear OA(539, 1953138, F5, 6) (dual of [1953138, 1953099, 7]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(538, 1953136, F5, 6) (dual of [1953136, 1953098, 7]-code), using
    • construction X4 applied to Ce(5) ⊂ Ce(3) [i] based on
      1. linear OA(537, 1953125, F5, 6) (dual of [1953125, 1953088, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 1953124 = 59−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
      2. linear OA(528, 1953125, F5, 4) (dual of [1953125, 1953097, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 1953124 = 59−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
      3. linear OA(510, 11, F5, 10) (dual of [11, 1, 11]-code or 11-arc in PG(9,5)), using
      4. linear OA(51, 11, F5, 1) (dual of [11, 10, 2]-code), using
  2. linear OA(538, 1953137, F5, 5) (dual of [1953137, 1953099, 6]-code), using Gilbert–VarÅ¡amov bound and bm = 538 > Vbs−1(k−1) = 155 223528 567291 336789 158465 [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, 1953138, F5, 2, 6) (dual of [(1953138, 2), 3906237, 7]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(539, 1953138, F5, 3, 6) (dual of [(1953138, 3), 5859375, 7]-NRT-code) [i]
3Digital (33, 39, 1953138)-net over F5 [i]
4Linear OOA(539, 976569, F5, 2, 6) (dual of [(976569, 2), 1953099, 7]-NRT-code) [i]OOA Folding