Information on Result #737252

Linear OA(4252, 16452, F4, 45) (dual of [16452, 16200, 46]-code), using construction X applied to Ce(44) ⊂ Ce(34) based on
  1. linear OA(4232, 16384, F4, 45) (dual of [16384, 16152, 46]-code), using an extension Ce(44) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,44], and designed minimum distance d ≥ |I|+1 = 45 [i]
  2. linear OA(4183, 16384, F4, 35) (dual of [16384, 16201, 36]-code), using an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [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(4252, 16452, F4, 2, 45) (dual of [(16452, 2), 32652, 46]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(4252, 16452, F4, 3, 45) (dual of [(16452, 3), 49104, 46]-NRT-code) [i]
3Digital (207, 252, 16452)-net over F4 [i]
4Linear OOA(4252, 8226, F4, 2, 45) (dual of [(8226, 2), 16200, 46]-NRT-code) [i]OOA Folding
5Linear OOA(4252, 5484, F4, 3, 45) (dual of [(5484, 3), 16200, 46]-NRT-code) [i]