Information on Result #1302921

Linear OA(8146, 2097187, F8, 23) (dual of [2097187, 2097041, 24]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(8145, 2097185, F8, 23) (dual of [2097185, 2097040, 24]-code), using
    • construction X applied to C([0,11]) ⊂ C([0,9]) [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(8113, 2097153, F8, 19) (dual of [2097153, 2097040, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153 | 814−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
      3. linear OA(84, 32, F8, 3) (dual of [32, 28, 4]-code or 32-cap in PG(3,8)), using
  2. linear OA(8145, 2097186, F8, 22) (dual of [2097186, 2097041, 23]-code), using Gilbert–VarÅ¡amov bound and bm = 8145 > Vbs−1(k−1) = 62093 145466 702123 406103 014560 578405 360638 098480 021164 766781 354407 003667 699228 959687 395769 078965 316525 242992 250299 145786 904866 792184 [i]
  3. linear OA(80, 1, F8, 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(8146, 2097187, F8, 2, 23) (dual of [(2097187, 2), 4194228, 24]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(8146, 2097187, F8, 3, 23) (dual of [(2097187, 3), 6291415, 24]-NRT-code) [i]
3Digital (123, 146, 2097187)-net over F8 [i]