Information on Result #2226557
Linear OA(2212, 525, F2, 50) (dual of [525, 313, 51]-code), using 1 times truncation based on linear OA(2213, 526, F2, 51) (dual of [526, 313, 52]-code), using
- construction X applied to Ce(50) ⊂ Ce(46) [i] based on
- linear OA(2208, 512, F2, 51) (dual of [512, 304, 52]-code), using an extension Ce(50) of the primitive narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [1,50], and designed minimum distance d ≥ |I|+1 = 51 [i]
- linear OA(2199, 512, F2, 47) (dual of [512, 313, 48]-code), using an extension Ce(46) of the primitive narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [1,46], and designed minimum distance d ≥ |I|+1 = 47 [i]
- linear OA(25, 14, F2, 3) (dual of [14, 9, 4]-code or 14-cap in PG(4,2)), using
- discarding factors / shortening the dual code based on linear OA(25, 16, F2, 3) (dual of [16, 11, 4]-code or 16-cap in PG(4,2)), 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 OA(2214, 527, F2, 50) (dual of [527, 313, 51]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(2237, 582, F2, 50) (dual of [582, 345, 51]-code) | [i] | Varšamov–Edel Lengthening | |
| 3 | Linear OOA(2212, 262, F2, 2, 50) (dual of [(262, 2), 312, 51]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(2212, 175, F2, 3, 50) (dual of [(175, 3), 313, 51]-NRT-code) | [i] | ||
| 5 | Linear OOA(2212, 131, F2, 4, 50) (dual of [(131, 4), 312, 51]-NRT-code) | [i] | ||
| 6 | Linear OOA(2212, 105, F2, 5, 50) (dual of [(105, 5), 313, 51]-NRT-code) | [i] | ||