Information on Result #735220

Linear OA(8176, 6977, F81, 27) (dual of [6977, 6901, 28]-code), using (u, u+v)-construction based on
  1. linear OA(8123, 414, F81, 13) (dual of [414, 391, 14]-code), using
    • construction XX applied to C1 = C([36,47]), C2 = C([35,46]), C3 = C1 + C2 = C([36,46]), and C∩ = C1 ∩ C2 = C([35,47]) [i] based on
      1. linear OA(8121, 410, F81, 12) (dual of [410, 389, 13]-code), using the BCH-code C(I) with length 410 | 812−1, defining interval I = {36,37,…,47}, and designed minimum distance d ≥ |I|+1 = 13 [i]
      2. linear OA(8121, 410, F81, 12) (dual of [410, 389, 13]-code), using the BCH-code C(I) with length 410 | 812−1, defining interval I = {35,36,…,46}, and designed minimum distance d ≥ |I|+1 = 13 [i]
      3. linear OA(8123, 410, F81, 13) (dual of [410, 387, 14]-code), using the BCH-code C(I) with length 410 | 812−1, defining interval I = {35,36,…,47}, and designed minimum distance d ≥ |I|+1 = 14 [i]
      4. linear OA(8119, 410, F81, 11) (dual of [410, 391, 12]-code), using the BCH-code C(I) with length 410 | 812−1, defining interval I = {36,37,…,46}, and designed minimum distance d ≥ |I|+1 = 12 [i]
      5. linear OA(810, 2, F81, 0) (dual of [2, 2, 1]-code), using
      6. linear OA(810, 2, F81, 0) (dual of [2, 2, 1]-code) (see above)
  2. linear OA(8153, 6563, F81, 27) (dual of [6563, 6510, 28]-code), using
    • construction X applied to Ce(26) ⊂ Ce(25) [i] based on
      1. linear OA(8153, 6561, F81, 27) (dual of [6561, 6508, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
      2. linear OA(8151, 6561, F81, 26) (dual of [6561, 6510, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
      3. linear OA(810, 2, F81, 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(8176, 3488, F81, 2, 27) (dual of [(3488, 2), 6900, 28]-NRT-code) [i]OOA Folding
2Linear OOA(8176, 2325, F81, 3, 27) (dual of [(2325, 3), 6899, 28]-NRT-code) [i]