Information on Result #734831

Linear OA(6477, 4687, F64, 27) (dual of [4687, 4610, 28]-code), using (u, u+v)-construction based on
  1. linear OA(6424, 589, F64, 13) (dual of [589, 565, 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(6422, 585, F64, 12) (dual of [585, 563, 13]-code), using the BCH-code C(I) with length 585 | 642−1, defining interval I = {27,28,…,38}, and designed minimum distance d ≥ |I|+1 = 13 [i]
      2. linear OA(6422, 585, F64, 12) (dual of [585, 563, 13]-code), using the BCH-code C(I) with length 585 | 642−1, defining interval I = {26,27,…,37}, and designed minimum distance d ≥ |I|+1 = 13 [i]
      3. linear OA(6424, 585, F64, 13) (dual of [585, 561, 14]-code), using the BCH-code C(I) with length 585 | 642−1, defining interval I = {26,27,…,38}, and designed minimum distance d ≥ |I|+1 = 14 [i]
      4. linear OA(6420, 585, F64, 11) (dual of [585, 565, 12]-code), using the BCH-code C(I) with length 585 | 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(6453, 4098, F64, 27) (dual of [4098, 4045, 28]-code), using
    • construction X applied to Ce(26) ⊂ Ce(25) [i] based on
      1. linear OA(6453, 4096, F64, 27) (dual of [4096, 4043, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
      2. 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]
      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(6477, 2343, F64, 2, 27) (dual of [(2343, 2), 4609, 28]-NRT-code) [i]OOA Folding
2Linear OOA(6477, 1562, F64, 3, 27) (dual of [(1562, 3), 4609, 28]-NRT-code) [i]