Information on Result #2960643
Linear OOA(2223, 599189, F2, 7, 21) (dual of [(599189, 7), 4194100, 22]-NRT-code), using 21 times duplication based on linear OOA(2222, 599189, F2, 7, 21) (dual of [(599189, 7), 4194101, 22]-NRT-code), using
- OOA 7-folding [i] based on linear OA(2222, 4194323, F2, 21) (dual of [4194323, 4194101, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(2222, 4194327, F2, 21) (dual of [4194327, 4194105, 22]-code), using
- construction X applied to Ce(20) ⊂ Ce(18) [i] based on
- linear OA(2221, 4194304, F2, 21) (dual of [4194304, 4194083, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 222−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(2199, 4194304, F2, 19) (dual of [4194304, 4194105, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 222−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(21, 23, F2, 1) (dual of [23, 22, 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(20) ⊂ Ce(18) [i] based on
- discarding factors / shortening the dual code based on linear OA(2222, 4194327, F2, 21) (dual of [4194327, 4194105, 22]-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(2223, 569012, F2, 8, 21) (dual of [(569012, 8), 4551873, 22]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (202, 223, 569012)-net over F2 | [i] | ||