Information on Result #1303322

Linear OA(989, 59083, F9, 19) (dual of [59083, 58994, 20]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(988, 59081, F9, 19) (dual of [59081, 58993, 20]-code), using
    • construction X applied to Ce(18) ⊂ Ce(12) [i] based on
      1. linear OA(981, 59049, F9, 19) (dual of [59049, 58968, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
      2. linear OA(956, 59049, F9, 13) (dual of [59049, 58993, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
      3. linear OA(97, 32, F9, 5) (dual of [32, 25, 6]-code), using
  2. linear OA(988, 59082, F9, 18) (dual of [59082, 58994, 19]-code), using Gilbert–VarÅ¡amov bound and bm = 988 > Vbs−1(k−1) = 8224 136702 443124 395013 884791 154226 847088 382657 031931 169574 707289 403894 849757 896521 [i]
  3. linear OA(90, 1, F9, 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(989, 59083, F9, 2, 19) (dual of [(59083, 2), 118077, 20]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(989, 59083, F9, 3, 19) (dual of [(59083, 3), 177160, 20]-NRT-code) [i]
3Digital (70, 89, 59083)-net over F9 [i]