Information on Result #1303336

Linear OA(993, 13136, F9, 23) (dual of [13136, 13043, 24]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(992, 13134, F9, 23) (dual of [13134, 13042, 24]-code), using
    • trace code [i] based on linear OA(8146, 6567, F81, 23) (dual of [6567, 6521, 24]-code), using
      • construction X applied to C([0,11]) ⊂ C([0,10]) [i] based on
        1. linear OA(8145, 6562, F81, 23) (dual of [6562, 6517, 24]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 814−1, defining interval I = [0,11], and minimum distance d ≥ |{−11,−10,…,11}|+1 = 24 (BCH-bound) [i]
        2. linear OA(8141, 6562, F81, 21) (dual of [6562, 6521, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 814−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
        3. linear OA(811, 5, F81, 1) (dual of [5, 4, 2]-code), using
  2. linear OA(992, 13135, F9, 22) (dual of [13135, 13043, 23]-code), using Gilbert–VarÅ¡amov bound and bm = 992 > Vbs−1(k−1) = 54 453078 812243 103384 477486 137889 149135 990583 712112 993013 357559 294839 274025 392619 229489 [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(993, 13136, F9, 2, 23) (dual of [(13136, 2), 26179, 24]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(993, 13136, F9, 3, 23) (dual of [(13136, 3), 39315, 24]-NRT-code) [i]
3Digital (70, 93, 13136)-net over F9 [i]
4Linear OOA(993, 6568, F9, 2, 23) (dual of [(6568, 2), 13043, 24]-NRT-code) [i]OOA Folding