Information on Result #948685
Linear OOA(2256, 687, F2, 3, 46) (dual of [(687, 3), 1805, 47]-NRT-code), using OOA 3-folding based on linear OA(2256, 2061, F2, 46) (dual of [2061, 1805, 47]-code), using
- 2 times code embedding in larger space [i] based on linear OA(2254, 2059, F2, 46) (dual of [2059, 1805, 47]-code), using
- 1 times truncation [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
- 1 times truncation [i] based on linear OA(2255, 2060, F2, 47) (dual of [2060, 1805, 48]-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(2257, 687, F2, 3, 46) (dual of [(687, 3), 1804, 47]-NRT-code) | [i] | OOA Duplication | |
| 2 | Linear OOA(2258, 687, F2, 3, 46) (dual of [(687, 3), 1803, 47]-NRT-code) | [i] | ||