Information on Result #2480912
Linear OOA(2258, 1031, F2, 2, 46) (dual of [(1031, 2), 1804, 47]-NRT-code), using 21 times duplication based on linear OOA(2257, 1031, F2, 2, 46) (dual of [(1031, 2), 1805, 47]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(2255, 1030, F2, 2, 46) (dual of [(1030, 2), 1805, 47]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2255, 2060, F2, 46) (dual of [2060, 1805, 47]-code), using
- strength reduction [i] based on linear OA(2255, 2060, F2, 47) (dual of [2060, 1805, 48]-code), using
- construction X applied to Ce(46) ⊂ Ce(44) [i] based on
- linear OA(2254, 2048, F2, 47) (dual of [2048, 1794, 48]-code), using an extension Ce(46) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,46], and designed minimum distance d ≥ |I|+1 = 47 [i]
- linear OA(2243, 2048, F2, 45) (dual of [2048, 1805, 46]-code), using an extension Ce(44) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,44], and designed minimum distance d ≥ |I|+1 = 45 [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(46) ⊂ Ce(44) [i] based on
- strength reduction [i] based on linear OA(2255, 2060, F2, 47) (dual of [2060, 1805, 48]-code), using
- OOA 2-folding [i] based on linear OA(2255, 2060, F2, 46) (dual of [2060, 1805, 47]-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(2258, 985, F2, 3, 46) (dual of [(985, 3), 2697, 47]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2258, 985, F2, 4, 46) (dual of [(985, 4), 3682, 47]-NRT-code) | [i] | ||
| 3 | Linear OOA(2258, 985, F2, 5, 46) (dual of [(985, 5), 4667, 47]-NRT-code) | [i] | ||
| 4 | Linear OOA(2258, 985, F2, 6, 46) (dual of [(985, 6), 5652, 47]-NRT-code) | [i] | ||
| 5 | Linear OOA(2258, 985, F2, 7, 46) (dual of [(985, 7), 6637, 47]-NRT-code) | [i] | ||
| 6 | Linear OOA(2258, 985, F2, 8, 46) (dual of [(985, 8), 7622, 47]-NRT-code) | [i] | ||
| 7 | Digital (212, 258, 985)-net over F2 | [i] | ||