Information on Result #1301591

Linear OA(592, 15657, F5, 18) (dual of [15657, 15565, 19]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(591, 15655, F5, 18) (dual of [15655, 15564, 19]-code), using
    • construction X applied to Ce(17) ⊂ Ce(12) [i] based on
      1. linear OA(585, 15625, F5, 18) (dual of [15625, 15540, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
      2. linear OA(561, 15625, F5, 13) (dual of [15625, 15564, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
      3. linear OA(56, 30, F5, 4) (dual of [30, 24, 5]-code), using
  2. linear OA(591, 15656, F5, 17) (dual of [15656, 15565, 18]-code), using Gilbert–VarÅ¡amov bound and bm = 591 > Vbs−1(k−1) = 2651 981039 445899 085248 112238 386894 825342 529785 192013 710595 221165 [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(592, 15657, F5, 2, 18) (dual of [(15657, 2), 31222, 19]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(592, 15657, F5, 3, 18) (dual of [(15657, 3), 46879, 19]-NRT-code) [i]
3Digital (74, 92, 15657)-net over F5 [i]