Information on Result #730239

Linear OA(8127, 414, F81, 15) (dual of [414, 387, 16]-code), using construction XX applied to C1 = C([34,47]), C2 = C([33,46]), C3 = C1 + C2 = C([34,46]), and C∩ = C1 ∩ C2 = C([33,47]) based on
  1. linear OA(8125, 410, F81, 14) (dual of [410, 385, 15]-code), using the BCH-code C(I) with length 410 | 812−1, defining interval I = {34,35,…,47}, and designed minimum distance d ≥ |I|+1 = 15 [i]
  2. linear OA(8125, 410, F81, 14) (dual of [410, 385, 15]-code), using the BCH-code C(I) with length 410 | 812−1, defining interval I = {33,34,…,46}, and designed minimum distance d ≥ |I|+1 = 15 [i]
  3. linear OA(8127, 410, F81, 15) (dual of [410, 383, 16]-code), using the BCH-code C(I) with length 410 | 812−1, defining interval I = {33,34,…,47}, and designed minimum distance d ≥ |I|+1 = 16 [i]
  4. 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 = {34,35,…,46}, and designed minimum distance d ≥ |I|+1 = 14 [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)

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(8127, 414, F81, 2, 15) (dual of [(414, 2), 801, 16]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(8127, 414, F81, 3, 15) (dual of [(414, 3), 1215, 16]-NRT-code) [i]
3Linear OOA(8127, 414, F81, 4, 15) (dual of [(414, 4), 1629, 16]-NRT-code) [i]
4Digital (12, 27, 414)-net over F81 [i]
5Linear OA(8128, 505, F81, 15) (dual of [505, 477, 16]-code) [i]VarÅ¡amov–Edel Lengthening
6Linear OOA(8127, 207, F81, 2, 15) (dual of [(207, 2), 387, 16]-NRT-code) [i]OOA Folding
7Linear OOA(8127, 138, F81, 3, 15) (dual of [(138, 3), 387, 16]-NRT-code) [i]