Information on Result #678503

Linear OA(4247, 262228, F4, 34) (dual of [262228, 261981, 35]-code), using construction X applied to Ce(33) ⊂ Ce(24) based on
  1. linear OA(4226, 262144, F4, 34) (dual of [262144, 261918, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
  2. linear OA(4163, 262144, F4, 25) (dual of [262144, 261981, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
  3. linear OA(421, 84, F4, 8) (dual of [84, 63, 9]-code), using
    • 1 times truncation [i] based on linear OA(422, 85, F4, 9) (dual of [85, 63, 10]-code), using
      • the BCH-code C(I) with length 85 | 44−1, defining interval I = {−20,−17,−14,…,4}, and designed minimum distance d ≥ |I|+1 = 10 [i]

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(4248, 262229, F4, 34) (dual of [262229, 261981, 35]-code) [i]Code Embedding in Larger Space
2Linear OA(4249, 262230, F4, 34) (dual of [262230, 261981, 35]-code) [i]
3Linear OA(4250, 262231, F4, 34) (dual of [262231, 261981, 35]-code) [i]
4Linear OA(4250, 262232, F4, 34) (dual of [262232, 261982, 35]-code) [i]Construction X with VarÅ¡amov Bound
5Linear OOA(4247, 131114, F4, 2, 34) (dual of [(131114, 2), 261981, 35]-NRT-code) [i]OOA Folding
6Linear OOA(4247, 87409, F4, 3, 34) (dual of [(87409, 3), 261980, 35]-NRT-code) [i]
7Linear OOA(4247, 15425, F4, 34, 34) (dual of [(15425, 34), 524203, 35]-NRT-code) [i]OA Folding and Stacking