Information on Result #1315801
Linear OA(6449, 4318, F64, 21) (dual of [4318, 4269, 22]-code), using 212 step Varšamov–Edel lengthening with (ri) = (4, 0, 1, 4 times 0, 1, 16 times 0, 1, 49 times 0, 1, 137 times 0) based on linear OA(6441, 4098, F64, 21) (dual of [4098, 4057, 22]-code), using
- construction X applied to Ce(20) ⊂ Ce(19) [i] based on
- linear OA(6441, 4096, F64, 21) (dual of [4096, 4055, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(6439, 4096, F64, 20) (dual of [4096, 4057, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [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
Mode: 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(6449, 4318, F64, 2, 21) (dual of [(4318, 2), 8587, 22]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(6449, 4318, F64, 3, 21) (dual of [(4318, 3), 12905, 22]-NRT-code) | [i] | ||
| 3 | Digital (28, 49, 4318)-net over F64 | [i] | ||
| 4 | Linear OOA(6449, 2159, F64, 2, 21) (dual of [(2159, 2), 4269, 22]-NRT-code) | [i] | OOA Folding | |