Information on Result #1301454

Linear OA(569, 1953159, F5, 9) (dual of [1953159, 1953090, 10]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(567, 1953155, F5, 9) (dual of [1953155, 1953088, 10]-code), using
    • construction X applied to Ce(8) ⊂ Ce(5) [i] based on
      1. linear OA(564, 1953125, F5, 9) (dual of [1953125, 1953061, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 1953124 = 59−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
      2. 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]
      3. linear OA(53, 30, F5, 2) (dual of [30, 27, 3]-code), using
  2. linear OA(567, 1953157, F5, 8) (dual of [1953157, 1953090, 9]-code), using Gilbert–VarÅ¡amov bound and bm = 567 > Vbs−1(k−1) = 352 487440 432224 926005 528414 053846 012945 165425 [i]
  3. linear OA(50, 2, F5, 0) (dual of [2, 2, 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(569, 1953159, F5, 2, 9) (dual of [(1953159, 2), 3906249, 10]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(569, 1953159, F5, 3, 9) (dual of [(1953159, 3), 5859408, 10]-NRT-code) [i]
3Digital (60, 69, 1953159)-net over F5 [i]