Information on Result #1303176

Linear OA(961, 13136, F9, 15) (dual of [13136, 13075, 16]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(960, 13134, F9, 15) (dual of [13134, 13074, 16]-code), using
    • trace code [i] based on linear OA(8130, 6567, F81, 15) (dual of [6567, 6537, 16]-code), using
      • construction X applied to C([0,7]) ⊂ C([0,6]) [i] based on
        1. linear OA(8129, 6562, F81, 15) (dual of [6562, 6533, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 814−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
        2. linear OA(8125, 6562, F81, 13) (dual of [6562, 6537, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 814−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
        3. linear OA(811, 5, F81, 1) (dual of [5, 4, 2]-code), using
  2. linear OA(960, 13135, F9, 14) (dual of [13135, 13075, 15]-code), using Gilbert–VarÅ¡amov bound and bm = 960 > Vbs−1(k−1) = 30 375571 288920 254702 038083 474426 714481 454719 794757 341489 [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(961, 13136, F9, 2, 15) (dual of [(13136, 2), 26211, 16]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(961, 13136, F9, 3, 15) (dual of [(13136, 3), 39347, 16]-NRT-code) [i]
3Digital (46, 61, 13136)-net over F9 [i]
4Linear OOA(961, 6568, F9, 2, 15) (dual of [(6568, 2), 13075, 16]-NRT-code) [i]OOA Folding