Information on Result #734958

Linear OA(6458, 4297, F64, 21) (dual of [4297, 4239, 22]-code), using (u, u+v)-construction based on
  1. linear OA(6417, 199, F64, 10) (dual of [199, 182, 11]-code), using
    • construction XX applied to C1 = C([61,69]), C2 = C([60,68]), C3 = C1 + C2 = C([61,68]), and C∩ = C1 ∩ C2 = C([60,69]) [i] based on
      1. linear OA(6415, 195, F64, 9) (dual of [195, 180, 10]-code), using the BCH-code C(I) with length 195 | 642−1, defining interval I = {61,62,…,69}, and designed minimum distance d ≥ |I|+1 = 10 [i]
      2. linear OA(6415, 195, F64, 9) (dual of [195, 180, 10]-code), using the BCH-code C(I) with length 195 | 642−1, defining interval I = {60,61,…,68}, and designed minimum distance d ≥ |I|+1 = 10 [i]
      3. linear OA(6417, 195, F64, 10) (dual of [195, 178, 11]-code), using the BCH-code C(I) with length 195 | 642−1, defining interval I = {60,61,…,69}, and designed minimum distance d ≥ |I|+1 = 11 [i]
      4. linear OA(6413, 195, F64, 8) (dual of [195, 182, 9]-code), using the BCH-code C(I) with length 195 | 642−1, defining interval I = {61,62,…,68}, and designed minimum distance d ≥ |I|+1 = 9 [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(6441, 4098, F64, 21) (dual of [4098, 4057, 22]-code), using
    • construction X applied to Ce(20) ⊂ Ce(19) [i] based on
      1. linear OA(6441, 4096, F64, 21) (dual of [4096, 4055, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
      2. linear OA(6439, 4096, F64, 20) (dual of [4096, 4057, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [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(6458, 2148, F64, 2, 21) (dual of [(2148, 2), 4238, 22]-NRT-code) [i]OOA Folding
2Linear OOA(6458, 1432, F64, 3, 21) (dual of [(1432, 3), 4238, 22]-NRT-code) [i]