Information on Result #734845

Linear OA(6474, 4417, F64, 26) (dual of [4417, 4343, 27]-code), using (u, u+v)-construction based on
  1. linear OA(6423, 319, F64, 13) (dual of [319, 296, 14]-code), using
    • construction XX applied to C1 = C([314,10]), C2 = C([0,11]), C3 = C1 + C2 = C([0,10]), and C∩ = C1 ∩ C2 = C([314,11]) [i] based on
      1. linear OA(6421, 315, F64, 12) (dual of [315, 294, 13]-code), using the BCH-code C(I) with length 315 | 642−1, defining interval I = {−1,0,…,10}, and designed minimum distance d ≥ |I|+1 = 13 [i]
      2. linear OA(6421, 315, F64, 12) (dual of [315, 294, 13]-code), using the expurgated narrow-sense BCH-code C(I) with length 315 | 642−1, defining interval I = [0,11], and designed minimum distance d ≥ |I|+1 = 13 [i]
      3. linear OA(6423, 315, F64, 13) (dual of [315, 292, 14]-code), using the BCH-code C(I) with length 315 | 642−1, defining interval I = {−1,0,…,11}, and designed minimum distance d ≥ |I|+1 = 14 [i]
      4. linear OA(6419, 315, F64, 11) (dual of [315, 296, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 315 | 642−1, defining interval I = [0,10], 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(6474, 2208, F64, 2, 26) (dual of [(2208, 2), 4342, 27]-NRT-code) [i]OOA Folding
2Linear OOA(6474, 1472, F64, 3, 26) (dual of [(1472, 3), 4342, 27]-NRT-code) [i]