Information on Result #1302944

Linear OA(8150, 2097206, F8, 23) (dual of [2097206, 2097056, 24]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(8148, 2097202, F8, 23) (dual of [2097202, 2097054, 24]-code), using
    • construction X applied to C([0,11]) ⊂ C([0,8]) [i] based on
      1. linear OA(8141, 2097153, F8, 23) (dual of [2097153, 2097012, 24]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153 | 814−1, defining interval I = [0,11], and minimum distance d ≥ |{−11,−10,…,11}|+1 = 24 (BCH-bound) [i]
      2. linear OA(899, 2097153, F8, 17) (dual of [2097153, 2097054, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153 | 814−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
      3. linear OA(87, 49, F8, 5) (dual of [49, 42, 6]-code), using
  2. linear OA(8148, 2097204, F8, 22) (dual of [2097204, 2097056, 23]-code), using Gilbert–VarÅ¡amov bound and bm = 8148 > Vbs−1(k−1) = 62104 338248 432274 725446 143282 385669 454073 074287 546061 369035 750695 809152 503714 165512 030939 197814 196453 199960 437023 820274 912687 039472 [i]
  3. linear OA(80, 2, F8, 0) (dual of [2, 2, 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(8150, 2097206, F8, 2, 23) (dual of [(2097206, 2), 4194262, 24]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(8150, 2097206, F8, 3, 23) (dual of [(2097206, 3), 6291468, 24]-NRT-code) [i]
3Digital (127, 150, 2097206)-net over F8 [i]
4Linear OOA(8150, 1048603, F8, 2, 23) (dual of [(1048603, 2), 2097056, 24]-NRT-code) [i]OOA Folding