Information on Result #1300937

Linear OA(4227, 16446, F4, 40) (dual of [16446, 16219, 41]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(4224, 16440, F4, 40) (dual of [16440, 16216, 41]-code), using
    • construction X applied to C([0,20]) ⊂ C([0,16]) [i] based on
      1. linear OA(4211, 16385, F4, 41) (dual of [16385, 16174, 42]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 414−1, defining interval I = [0,20], and minimum distance d ≥ |{−20,−19,…,20}|+1 = 42 (BCH-bound) [i]
      2. linear OA(4169, 16385, F4, 33) (dual of [16385, 16216, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 414−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
      3. linear OA(413, 55, F4, 6) (dual of [55, 42, 7]-code), using
  2. linear OA(4224, 16443, F4, 39) (dual of [16443, 16219, 40]-code), using Gilbert–VarÅ¡amov bound and bm = 4224 > Vbs−1(k−1) = 39 821365 238914 168531 951313 719462 111168 843573 725219 539111 694287 426719 268487 085353 314936 884335 370330 497102 072402 578233 559990 809587 789556 [i]
  3. linear OA(40, 3, F4, 0) (dual of [3, 3, 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(4227, 16446, F4, 2, 40) (dual of [(16446, 2), 32665, 41]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(4227, 16446, F4, 3, 40) (dual of [(16446, 3), 49111, 41]-NRT-code) [i]
3Digital (187, 227, 16446)-net over F4 [i]
4Linear OOA(4227, 8223, F4, 2, 40) (dual of [(8223, 2), 16219, 41]-NRT-code) [i]OOA Folding