Information on Result #2790319
Linear OOA(2243, 4100, F2, 4, 34) (dual of [(4100, 4), 16157, 35]-NRT-code), using 22 times duplication based on linear OOA(2241, 4100, F2, 4, 34) (dual of [(4100, 4), 16159, 35]-NRT-code), using
- OOA 4-folding [i] based on linear OA(2241, 16400, F2, 34) (dual of [16400, 16159, 35]-code), using
- 2 times code embedding in larger space [i] based on linear OA(2239, 16398, F2, 34) (dual of [16398, 16159, 35]-code), using
- 1 times truncation [i] based on linear OA(2240, 16399, F2, 35) (dual of [16399, 16159, 36]-code), using
- construction X applied to Ce(34) ⊂ Ce(32) [i] based on
- linear OA(2239, 16384, F2, 35) (dual of [16384, 16145, 36]-code), using an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 16383 = 214−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(2225, 16384, F2, 33) (dual of [16384, 16159, 34]-code), using an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 16383 = 214−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(21, 15, F2, 1) (dual of [15, 14, 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(34) ⊂ Ce(32) [i] based on
- 1 times truncation [i] based on linear OA(2240, 16399, F2, 35) (dual of [16399, 16159, 36]-code), using
- 2 times code embedding in larger space [i] based on linear OA(2239, 16398, F2, 34) (dual of [16398, 16159, 35]-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(2243, 3490, F2, 5, 34) (dual of [(3490, 5), 17207, 35]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2243, 3490, F2, 6, 34) (dual of [(3490, 6), 20697, 35]-NRT-code) | [i] | ||
| 3 | Linear OOA(2243, 3490, F2, 7, 34) (dual of [(3490, 7), 24187, 35]-NRT-code) | [i] | ||
| 4 | Linear OOA(2243, 3490, F2, 8, 34) (dual of [(3490, 8), 27677, 35]-NRT-code) | [i] | ||
| 5 | Digital (209, 243, 3490)-net over F2 | [i] | ||