Information on Result #2478662
Linear OOA(2104, 1031, F2, 2, 18) (dual of [(1031, 2), 1958, 19]-NRT-code), using 21 times duplication based on linear OOA(2103, 1031, F2, 2, 18) (dual of [(1031, 2), 1959, 19]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(2101, 1030, F2, 2, 18) (dual of [(1030, 2), 1959, 19]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2101, 2060, F2, 18) (dual of [2060, 1959, 19]-code), using
- strength reduction [i] based on linear OA(2101, 2060, F2, 19) (dual of [2060, 1959, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(16) [i] based on
- linear OA(2100, 2048, F2, 19) (dual of [2048, 1948, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(289, 2048, F2, 17) (dual of [2048, 1959, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(21, 12, F2, 1) (dual of [12, 11, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(21, s, F2, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to Ce(18) ⊂ Ce(16) [i] based on
- strength reduction [i] based on linear OA(2101, 2060, F2, 19) (dual of [2060, 1959, 20]-code), using
- OOA 2-folding [i] based on linear OA(2101, 2060, F2, 18) (dual of [2060, 1959, 19]-code), using
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(2104, 695, F2, 3, 18) (dual of [(695, 3), 1981, 19]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2104, 695, F2, 4, 18) (dual of [(695, 4), 2676, 19]-NRT-code) | [i] | ||
| 3 | Linear OOA(2104, 695, F2, 5, 18) (dual of [(695, 5), 3371, 19]-NRT-code) | [i] | ||
| 4 | Linear OOA(2104, 695, F2, 6, 18) (dual of [(695, 6), 4066, 19]-NRT-code) | [i] | ||
| 5 | Linear OOA(2104, 695, F2, 7, 18) (dual of [(695, 7), 4761, 19]-NRT-code) | [i] | ||
| 6 | Linear OOA(2104, 695, F2, 8, 18) (dual of [(695, 8), 5456, 19]-NRT-code) | [i] | ||
| 7 | Digital (86, 104, 695)-net over F2 | [i] | ||