Information on Result #734777

Linear OA(6484, 4297, F64, 30) (dual of [4297, 4213, 31]-code), using (u, u+v)-construction based on
  1. linear OA(6425, 199, F64, 15) (dual of [199, 174, 16]-code), using
    • construction XX applied to C1 = C([59,72]), C2 = C([58,71]), C3 = C1 + C2 = C([59,71]), and C∩ = C1 ∩ C2 = C([58,72]) [i] based on
      1. linear OA(6423, 195, F64, 14) (dual of [195, 172, 15]-code), using the BCH-code C(I) with length 195 | 642−1, defining interval I = {59,60,…,72}, and designed minimum distance d ≥ |I|+1 = 15 [i]
      2. linear OA(6423, 195, F64, 14) (dual of [195, 172, 15]-code), using the BCH-code C(I) with length 195 | 642−1, defining interval I = {58,59,…,71}, and designed minimum distance d ≥ |I|+1 = 15 [i]
      3. linear OA(6425, 195, F64, 15) (dual of [195, 170, 16]-code), using the BCH-code C(I) with length 195 | 642−1, defining interval I = {58,59,…,72}, and designed minimum distance d ≥ |I|+1 = 16 [i]
      4. linear OA(6421, 195, F64, 13) (dual of [195, 174, 14]-code), using the BCH-code C(I) with length 195 | 642−1, defining interval I = {59,60,…,71}, and designed minimum distance d ≥ |I|+1 = 14 [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(6459, 4098, F64, 30) (dual of [4098, 4039, 31]-code), using
    • construction X applied to Ce(29) ⊂ Ce(28) [i] based on
      1. linear OA(6459, 4096, F64, 30) (dual of [4096, 4037, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
      2. linear OA(6457, 4096, F64, 29) (dual of [4096, 4039, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [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(6484, 2148, F64, 2, 30) (dual of [(2148, 2), 4212, 31]-NRT-code) [i]OOA Folding
2Linear OOA(6484, 1432, F64, 3, 30) (dual of [(1432, 3), 4212, 31]-NRT-code) [i]