Information on Result #1054493
Linear OOA(2251, 2052, F2, 4, 39) (dual of [(2052, 4), 7957, 40]-NRT-code), using OOA 4-folding based on linear OA(2251, 8208, F2, 39) (dual of [8208, 7957, 40]-code), using
- 2 times code embedding in larger space [i] based on linear OA(2249, 8206, F2, 39) (dual of [8206, 7957, 40]-code), using
- construction X applied to Ce(38) ⊂ Ce(36) [i] based on
- linear OA(2248, 8192, F2, 39) (dual of [8192, 7944, 40]-code), using an extension Ce(38) of the primitive narrow-sense BCH-code C(I) with length 8191 = 213−1, defining interval I = [1,38], and designed minimum distance d ≥ |I|+1 = 39 [i]
- linear OA(2235, 8192, F2, 37) (dual of [8192, 7957, 38]-code), using an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 8191 = 213−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(21, 14, F2, 1) (dual of [14, 13, 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(38) ⊂ Ce(36) [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(2252, 2052, F2, 4, 39) (dual of [(2052, 4), 7956, 40]-NRT-code) | [i] | OOA Duplication | |
| 2 | Linear OOA(2253, 2052, F2, 4, 39) (dual of [(2052, 4), 7955, 40]-NRT-code) | [i] | ||
| 3 | Linear OOA(2250, 2051, F2, 4, 38) (dual of [(2051, 4), 7954, 39]-NRT-code) | [i] | Truncation for OOAs | |
| 4 | Linear OOA(2251, 2032, F2, 5, 39) (dual of [(2032, 5), 9909, 40]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 5 | Linear OOA(2251, 2032, F2, 6, 39) (dual of [(2032, 6), 11941, 40]-NRT-code) | [i] | ||
| 6 | Linear OOA(2251, 2032, F2, 7, 39) (dual of [(2032, 7), 13973, 40]-NRT-code) | [i] | ||
| 7 | Linear OOA(2251, 2032, F2, 8, 39) (dual of [(2032, 8), 16005, 40]-NRT-code) | [i] | ||
| 8 | Digital (212, 251, 2032)-net over F2 | [i] | ||