Information on Result #874060
Linear OOA(6438, 2053, F64, 2, 18) (dual of [(2053, 2), 4068, 19]-NRT-code), using OOA 2-folding based on linear OA(6438, 4106, F64, 18) (dual of [4106, 4068, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(6438, 4107, F64, 18) (dual of [4107, 4069, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(13) [i] based on
- linear OA(6435, 4096, F64, 18) (dual of [4096, 4061, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(6427, 4096, F64, 14) (dual of [4096, 4069, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(643, 11, F64, 3) (dual of [11, 8, 4]-code or 11-arc in PG(2,64) or 11-cap in PG(2,64)), using
- discarding factors / shortening the dual code based on linear OA(643, 64, F64, 3) (dual of [64, 61, 4]-code or 64-arc in PG(2,64) or 64-cap in PG(2,64)), using
- Reed–Solomon code RS(61,64) [i]
- discarding factors / shortening the dual code based on linear OA(643, 64, F64, 3) (dual of [64, 61, 4]-code or 64-arc in PG(2,64) or 64-cap in PG(2,64)), using
- construction X applied to Ce(17) ⊂ Ce(13) [i] based on
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(6438, 2053, F64, 3, 18) (dual of [(2053, 3), 6121, 19]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (20, 38, 2053)-net over F64 | [i] | ||