Information on Result #946102
Linear OOA(2102, 345, F2, 3, 21) (dual of [(345, 3), 933, 22]-NRT-code), using OOA 3-folding based on linear OA(2102, 1035, F2, 21) (dual of [1035, 933, 22]-code), using
- construction X applied to Ce(20) ⊂ Ce(18) [i] based on
- linear OA(2101, 1024, F2, 21) (dual of [1024, 923, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(291, 1024, F2, 19) (dual of [1024, 933, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(21, 11, F2, 1) (dual of [11, 10, 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
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(2102, 345, F2, 4, 21) (dual of [(345, 4), 1278, 22]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2102, 345, F2, 5, 21) (dual of [(345, 5), 1623, 22]-NRT-code) | [i] | ||
| 3 | Linear OOA(2102, 345, F2, 6, 21) (dual of [(345, 6), 1968, 22]-NRT-code) | [i] | ||
| 4 | Linear OOA(2102, 345, F2, 7, 21) (dual of [(345, 7), 2313, 22]-NRT-code) | [i] | ||
| 5 | Linear OOA(2102, 345, F2, 8, 21) (dual of [(345, 8), 2658, 22]-NRT-code) | [i] | ||
| 6 | Digital (81, 102, 345)-net over F2 | [i] | ||