Information on Result #737268

Linear OA(4190, 16454, F4, 33) (dual of [16454, 16264, 34]-code), using construction X applied to Ce(32) ⊂ Ce(22) based on
  1. linear OA(4169, 16384, F4, 33) (dual of [16384, 16215, 34]-code), using an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [i]
  2. linear OA(4120, 16384, F4, 23) (dual of [16384, 16264, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
  3. linear OA(421, 70, F4, 9) (dual of [70, 49, 10]-code), using
    • construction XX applied to Ce(8) ⊂ Ce(6) ⊂ Ce(5) [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(413, 64, F4, 6) (dual of [64, 51, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
      4. linear OA(41, 5, F4, 1) (dual of [5, 4, 2]-code), using
      5. linear OA(40, 1, F4, 0) (dual of [1, 1, 1]-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 OA(4192, 16456, F4, 33) (dual of [16456, 16264, 34]-code) [i]Code Embedding in Larger Space
2Linear OA(4189, 16453, F4, 32) (dual of [16453, 16264, 33]-code) [i]Truncation
3Linear OOA(4190, 16454, F4, 2, 33) (dual of [(16454, 2), 32718, 34]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
4Linear OOA(4190, 16454, F4, 3, 33) (dual of [(16454, 3), 49172, 34]-NRT-code) [i]
5Digital (157, 190, 16454)-net over F4 [i]
6Linear OOA(4190, 8227, F4, 2, 33) (dual of [(8227, 2), 16264, 34]-NRT-code) [i]OOA Folding