Information on Result #1303256

Linear OA(977, 1062900, F9, 13) (dual of [1062900, 1062823, 14]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(976, 1062898, F9, 13) (dual of [1062898, 1062822, 14]-code), using
    • trace code [i] based on linear OA(8138, 531449, F81, 13) (dual of [531449, 531411, 14]-code), using
      • construction X applied to C([0,6]) ⊂ C([0,5]) [i] based on
        1. linear OA(8137, 531442, F81, 13) (dual of [531442, 531405, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442 | 816−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
        2. linear OA(8131, 531442, F81, 11) (dual of [531442, 531411, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442 | 816−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
        3. linear OA(811, 7, F81, 1) (dual of [7, 6, 2]-code), using
  2. linear OA(976, 1062899, F9, 12) (dual of [1062899, 1062823, 13]-code), using Gilbert–VarÅ¡amov bound and bm = 976 > Vbs−1(k−1) = 420 939534 469201 543845 633548 125825 226705 965928 413623 471188 022427 072977 [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, 1062900, F9, 2, 13) (dual of [(1062900, 2), 2125723, 14]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(977, 1062900, F9, 3, 13) (dual of [(1062900, 3), 3188623, 14]-NRT-code) [i]
3Digital (64, 77, 1062900)-net over F9 [i]
4Linear OOA(977, 531450, F9, 2, 13) (dual of [(531450, 2), 1062823, 14]-NRT-code) [i]OOA Folding