Information on Result #1303043

Linear OA(8167, 32797, F8, 37) (dual of [32797, 32630, 38]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(8165, 32793, F8, 37) (dual of [32793, 32628, 38]-code), using
    • construction X applied to C([0,18]) ⊂ C([0,16]) [i] based on
      1. linear OA(8161, 32769, F8, 37) (dual of [32769, 32608, 38]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769 | 810−1, defining interval I = [0,18], and minimum distance d ≥ |{−18,−17,…,18}|+1 = 38 (BCH-bound) [i]
      2. linear OA(8141, 32769, F8, 33) (dual of [32769, 32628, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769 | 810−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
      3. linear OA(84, 24, F8, 3) (dual of [24, 20, 4]-code or 24-cap in PG(3,8)), using
  2. linear OA(8165, 32795, F8, 36) (dual of [32795, 32630, 37]-code), using Gilbert–VarÅ¡amov bound and bm = 8165 > Vbs−1(k−1) = 4066 177743 899096 602683 464230 709518 922722 918364 629672 474993 222635 458244 035026 712435 827672 893229 011831 204599 818743 978020 956346 979582 723990 639619 788800 [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(8167, 32797, F8, 2, 37) (dual of [(32797, 2), 65427, 38]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(8167, 32797, F8, 3, 37) (dual of [(32797, 3), 98224, 38]-NRT-code) [i]
3Digital (130, 167, 32797)-net over F8 [i]
4Linear OOA(8167, 16398, F8, 2, 37) (dual of [(16398, 2), 32629, 38]-NRT-code) [i]OOA Folding