Information on Result #734844

Linear OA(6473, 4297, F64, 26) (dual of [4297, 4224, 27]-code), using (u, u+v)-construction based on
  1. linear OA(6422, 199, F64, 13) (dual of [199, 177, 14]-code), using
    • construction XX applied to C1 = C([27,38]), C2 = C([26,37]), C3 = C1 + C2 = C([27,37]), and C∩ = C1 ∩ C2 = C([26,38]) [i] based on
      1. linear OA(6420, 195, F64, 12) (dual of [195, 175, 13]-code), using the BCH-code C(I) with length 195 | 642−1, defining interval I = {27,28,…,38}, and designed minimum distance d ≥ |I|+1 = 13 [i]
      2. linear OA(6420, 195, F64, 12) (dual of [195, 175, 13]-code), using the BCH-code C(I) with length 195 | 642−1, defining interval I = {26,27,…,37}, and designed minimum distance d ≥ |I|+1 = 13 [i]
      3. linear OA(6422, 195, F64, 13) (dual of [195, 173, 14]-code), using the BCH-code C(I) with length 195 | 642−1, defining interval I = {26,27,…,38}, and designed minimum distance d ≥ |I|+1 = 14 [i]
      4. linear OA(6418, 195, F64, 11) (dual of [195, 177, 12]-code), using the BCH-code C(I) with length 195 | 642−1, defining interval I = {27,28,…,37}, and designed minimum distance d ≥ |I|+1 = 12 [i]
      5. linear OA(640, 2, F64, 0) (dual of [2, 2, 1]-code), using
      6. linear OA(640, 2, F64, 0) (dual of [2, 2, 1]-code) (see above)
  2. linear OA(6451, 4098, F64, 26) (dual of [4098, 4047, 27]-code), using
    • construction X applied to Ce(25) ⊂ Ce(24) [i] based on
      1. linear OA(6451, 4096, F64, 26) (dual of [4096, 4045, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
      2. linear OA(6449, 4096, F64, 25) (dual of [4096, 4047, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
      3. linear OA(640, 2, F64, 0) (dual of [2, 2, 1]-code) (see above)

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(6473, 2148, F64, 2, 26) (dual of [(2148, 2), 4223, 27]-NRT-code) [i]OOA Folding
2Linear OOA(6473, 1432, F64, 3, 26) (dual of [(1432, 3), 4223, 27]-NRT-code) [i]