Information on Result #1301363

Linear OA(557, 1953147, F5, 8) (dual of [1953147, 1953090, 9]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(556, 1953145, F5, 8) (dual of [1953145, 1953089, 9]-code), using
    • construction X4 applied to Ce(7) ⊂ Ce(5) [i] based on
      1. linear OA(555, 1953125, F5, 8) (dual of [1953125, 1953070, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 1953124 = 59−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [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(519, 20, F5, 19) (dual of [20, 1, 20]-code or 20-arc in PG(18,5)), using
      4. linear OA(51, 20, F5, 1) (dual of [20, 19, 2]-code), using
  2. linear OA(556, 1953146, F5, 7) (dual of [1953146, 1953090, 8]-code), using Gilbert–VarÅ¡amov bound and bm = 556 > Vbs−1(k−1) = 315 813991 606188 492913 084489 524271 265957 [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(557, 1953147, F5, 2, 8) (dual of [(1953147, 2), 3906237, 9]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(557, 1953147, F5, 3, 8) (dual of [(1953147, 3), 5859384, 9]-NRT-code) [i]
3Digital (49, 57, 1953147)-net over F5 [i]