Information on Result #2260229
Linear OA(2237, 2097, F2, 40) (dual of [2097, 1860, 41]-code), using 5 times code embedding in larger space based on linear OA(2232, 2092, F2, 40) (dual of [2092, 1860, 41]-code), using
- 1 times truncation [i] based on linear OA(2233, 2093, F2, 41) (dual of [2093, 1860, 42]-code), using
- construction X applied to Ce(40) ⊂ Ce(34) [i] based on
- linear OA(2221, 2048, F2, 41) (dual of [2048, 1827, 42]-code), using an extension Ce(40) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,40], and designed minimum distance d ≥ |I|+1 = 41 [i]
- linear OA(2188, 2048, F2, 35) (dual of [2048, 1860, 36]-code), using an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(212, 45, F2, 5) (dual of [45, 33, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(212, 48, F2, 5) (dual of [48, 36, 6]-code), using
- adding a parity check bit [i] based on linear OA(211, 47, F2, 4) (dual of [47, 36, 5]-code), using
- extracting embedded orthogonal array [i] based on digital (7, 11, 47)-net over F2, using
- adding a parity check bit [i] based on linear OA(211, 47, F2, 4) (dual of [47, 36, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(212, 48, F2, 5) (dual of [48, 36, 6]-code), using
- construction X applied to Ce(40) ⊂ Ce(34) [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(2237, 1062, F2, 2, 40) (dual of [(1062, 2), 1887, 41]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2237, 1062, F2, 3, 40) (dual of [(1062, 3), 2949, 41]-NRT-code) | [i] | ||
| 3 | Linear OOA(2237, 1062, F2, 4, 40) (dual of [(1062, 4), 4011, 41]-NRT-code) | [i] | ||
| 4 | Linear OOA(2237, 1062, F2, 5, 40) (dual of [(1062, 5), 5073, 41]-NRT-code) | [i] | ||
| 5 | Linear OOA(2237, 1062, F2, 6, 40) (dual of [(1062, 6), 6135, 41]-NRT-code) | [i] | ||
| 6 | Linear OOA(2237, 1062, F2, 7, 40) (dual of [(1062, 7), 7197, 41]-NRT-code) | [i] | ||
| 7 | Linear OOA(2237, 1062, F2, 8, 40) (dual of [(1062, 8), 8259, 41]-NRT-code) | [i] | ||
| 8 | Digital (197, 237, 1062)-net over F2 | [i] | ||