Information on Result #729793
Linear OA(6432, 319, F64, 18) (dual of [319, 287, 19]-code), using construction XX applied to C1 = C([314,15]), C2 = C([0,16]), C3 = C1 + C2 = C([0,15]), and C∩ = C1 ∩ C2 = C([314,16]) based on
- linear OA(6430, 315, F64, 17) (dual of [315, 285, 18]-code), using the BCH-code C(I) with length 315 | 642−1, defining interval I = {−1,0,…,15}, and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(6430, 315, F64, 17) (dual of [315, 285, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 315 | 642−1, defining interval I = [0,16], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(6432, 315, F64, 18) (dual of [315, 283, 19]-code), using the BCH-code C(I) with length 315 | 642−1, defining interval I = {−1,0,…,16}, and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(6428, 315, F64, 16) (dual of [315, 287, 17]-code), using the expurgated narrow-sense BCH-code C(I) with length 315 | 642−1, defining interval I = [0,15], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(640, 2, F64, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(640, s, F64, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- 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:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(6432, 319, F64, 2, 18) (dual of [(319, 2), 606, 19]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(6432, 319, F64, 3, 18) (dual of [(319, 3), 925, 19]-NRT-code) | [i] | ||
| 3 | Digital (14, 32, 319)-net over F64 | [i] | ||