Information on Result #1301642

Linear OA(598, 15657, F5, 19) (dual of [15657, 15559, 20]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(597, 15655, F5, 19) (dual of [15655, 15558, 20]-code), using
    • construction X applied to Ce(18) ⊂ Ce(13) [i] based on
      1. linear OA(591, 15625, F5, 19) (dual of [15625, 15534, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
      2. linear OA(567, 15625, F5, 14) (dual of [15625, 15558, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
      3. linear OA(56, 30, F5, 4) (dual of [30, 24, 5]-code), using
  2. linear OA(597, 15656, F5, 18) (dual of [15656, 15559, 19]-code), using Gilbert–VarÅ¡amov bound and bm = 597 > Vbs−1(k−1) = 9 758822 428038 598157 220133 455138 516909 720110 032514 725888 877394 683565 [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(598, 15657, F5, 2, 19) (dual of [(15657, 2), 31216, 20]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(598, 15657, F5, 3, 19) (dual of [(15657, 3), 46873, 20]-NRT-code) [i]
3Digital (79, 98, 15657)-net over F5 [i]