Information on Result #1303126

Linear OA(945, 13136, F9, 11) (dual of [13136, 13091, 12]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(944, 13134, F9, 11) (dual of [13134, 13090, 12]-code), using
    • trace code [i] based on linear OA(8122, 6567, F81, 11) (dual of [6567, 6545, 12]-code), using
      • construction X applied to C([0,5]) ⊂ C([0,4]) [i] based on
        1. linear OA(8121, 6562, F81, 11) (dual of [6562, 6541, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 814−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
        2. linear OA(8117, 6562, F81, 9) (dual of [6562, 6545, 10]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 814−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
        3. linear OA(811, 5, F81, 1) (dual of [5, 4, 2]-code), using
  2. linear OA(944, 13135, F9, 10) (dual of [13135, 13091, 11]-code), using Gilbert–VarÅ¡amov bound and bm = 944 > Vbs−1(k−1) = 4290 091281 856945 993538 717786 364526 301489 [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(945, 13136, F9, 2, 11) (dual of [(13136, 2), 26227, 12]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(945, 13136, F9, 3, 11) (dual of [(13136, 3), 39363, 12]-NRT-code) [i]
3Digital (34, 45, 13136)-net over F9 [i]
4Linear OOA(945, 6568, F9, 2, 11) (dual of [(6568, 2), 13091, 12]-NRT-code) [i]OOA Folding