Information on Result #737257

Linear OA(4231, 16452, F4, 41) (dual of [16452, 16221, 42]-code), using construction X applied to Ce(40) ⊂ Ce(30) based on
  1. linear OA(4211, 16384, F4, 41) (dual of [16384, 16173, 42]-code), using an extension Ce(40) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,40], and designed minimum distance d ≥ |I|+1 = 41 [i]
  2. linear OA(4162, 16384, F4, 31) (dual of [16384, 16222, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
  3. linear OA(420, 68, F4, 9) (dual of [68, 48, 10]-code), using
    • construction X applied to Ce(8) ⊂ Ce(6) [i] based on
      1. linear OA(419, 64, F4, 9) (dual of [64, 45, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
      2. linear OA(416, 64, F4, 7) (dual of [64, 48, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
      3. linear OA(41, 4, F4, 1) (dual of [4, 3, 2]-code), using

Mode: Constructive and 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(4231, 16452, F4, 2, 41) (dual of [(16452, 2), 32673, 42]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(4231, 16452, F4, 3, 41) (dual of [(16452, 3), 49125, 42]-NRT-code) [i]
3Digital (190, 231, 16452)-net over F4 [i]
4Linear OOA(4231, 8226, F4, 2, 41) (dual of [(8226, 2), 16221, 42]-NRT-code) [i]OOA Folding
5Linear OOA(4231, 5484, F4, 3, 41) (dual of [(5484, 3), 16221, 42]-NRT-code) [i]