Information on Result #1303254

Linear OA(977, 13136, F9, 19) (dual of [13136, 13059, 20]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(976, 13134, F9, 19) (dual of [13134, 13058, 20]-code), using
    • trace code [i] based on linear OA(8138, 6567, F81, 19) (dual of [6567, 6529, 20]-code), using
      • construction X applied to C([0,9]) ⊂ C([0,8]) [i] based on
        1. linear OA(8137, 6562, F81, 19) (dual of [6562, 6525, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 814−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
        2. linear OA(8133, 6562, F81, 17) (dual of [6562, 6529, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 814−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
        3. linear OA(811, 5, F81, 1) (dual of [5, 4, 2]-code), using
  2. linear OA(976, 13135, F9, 18) (dual of [13135, 13059, 19]-code), using Gilbert–VarÅ¡amov bound and bm = 976 > Vbs−1(k−1) = 64533 007435 981594 478124 168139 266388 015232 798430 043813 615160 566038 237489 [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(977, 13136, F9, 2, 19) (dual of [(13136, 2), 26195, 20]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(977, 13136, F9, 3, 19) (dual of [(13136, 3), 39331, 20]-NRT-code) [i]
3Digital (58, 77, 13136)-net over F9 [i]
4Linear OOA(977, 6568, F9, 2, 19) (dual of [(6568, 2), 13059, 20]-NRT-code) [i]OOA Folding