Information on Result #1097197
Linear OOA(2227, 3280, F2, 5, 33) (dual of [(3280, 5), 16173, 34]-NRT-code), using OOA 5-folding based on linear OA(2227, 16400, F2, 33) (dual of [16400, 16173, 34]-code), using
- 1 times code embedding in larger space [i] based on linear OA(2226, 16399, F2, 33) (dual of [16399, 16173, 34]-code), using
- construction X applied to Ce(32) ⊂ Ce(30) [i] based on
- 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(2211, 16384, F2, 31) (dual of [16384, 16173, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 16383 = 214−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [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(32) ⊂ Ce(30) [i] based on
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(2228, 3280, F2, 5, 33) (dual of [(3280, 5), 16172, 34]-NRT-code) | [i] | OOA Duplication | |
| 2 | Linear OOA(2229, 3280, F2, 5, 33) (dual of [(3280, 5), 16171, 34]-NRT-code) | [i] | ||
| 3 | Linear OOA(2230, 3280, F2, 5, 33) (dual of [(3280, 5), 16170, 34]-NRT-code) | [i] | ||
| 4 | Linear OOA(2227, 3223, F2, 6, 33) (dual of [(3223, 6), 19111, 34]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 5 | Linear OOA(2227, 3223, F2, 7, 33) (dual of [(3223, 7), 22334, 34]-NRT-code) | [i] | ||
| 6 | Linear OOA(2227, 3223, F2, 8, 33) (dual of [(3223, 8), 25557, 34]-NRT-code) | [i] | ||
| 7 | Digital (194, 227, 3223)-net over F2 | [i] | ||