Information on Result #1303148

Linear OA(953, 13136, F9, 13) (dual of [13136, 13083, 14]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(952, 13134, F9, 13) (dual of [13134, 13082, 14]-code), using
    • trace code [i] based on linear OA(8126, 6567, F81, 13) (dual of [6567, 6541, 14]-code), using
      • construction X applied to C([0,6]) ⊂ C([0,5]) [i] based on
        1. 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]
        2. 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]
        3. linear OA(811, 5, F81, 1) (dual of [5, 4, 2]-code), using
  2. linear OA(952, 13135, F9, 12) (dual of [13135, 13083, 13]-code), using Gilbert–VarÅ¡amov bound and bm = 952 > Vbs−1(k−1) = 429959 584804 971312 035988 248374 137515 635195 613489 [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(953, 13136, F9, 2, 13) (dual of [(13136, 2), 26219, 14]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(953, 13136, F9, 3, 13) (dual of [(13136, 3), 39355, 14]-NRT-code) [i]
3Digital (40, 53, 13136)-net over F9 [i]
4Linear OOA(953, 6568, F9, 2, 13) (dual of [(6568, 2), 13083, 14]-NRT-code) [i]OOA Folding