Information on Result #2667871
Linear OOA(2161, 1370, F2, 3, 27) (dual of [(1370, 3), 3949, 28]-NRT-code), using 22 times duplication based on linear OOA(2159, 1370, F2, 3, 27) (dual of [(1370, 3), 3951, 28]-NRT-code), using
- OOA 3-folding [i] based on linear OA(2159, 4110, F2, 27) (dual of [4110, 3951, 28]-code), using
- 1 times code embedding in larger space [i] based on linear OA(2158, 4109, F2, 27) (dual of [4109, 3951, 28]-code), using
- construction X applied to Ce(26) ⊂ Ce(24) [i] based on
- linear OA(2157, 4096, F2, 27) (dual of [4096, 3939, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(2145, 4096, F2, 25) (dual of [4096, 3951, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(21, 13, F2, 1) (dual of [13, 12, 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(26) ⊂ Ce(24) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(2158, 4109, F2, 27) (dual of [4109, 3951, 28]-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(2161, 1070, F2, 4, 27) (dual of [(1070, 4), 4119, 28]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2161, 1070, F2, 5, 27) (dual of [(1070, 5), 5189, 28]-NRT-code) | [i] | ||
| 3 | Linear OOA(2161, 1070, F2, 6, 27) (dual of [(1070, 6), 6259, 28]-NRT-code) | [i] | ||
| 4 | Linear OOA(2161, 1070, F2, 7, 27) (dual of [(1070, 7), 7329, 28]-NRT-code) | [i] | ||
| 5 | Linear OOA(2161, 1070, F2, 8, 27) (dual of [(1070, 8), 8399, 28]-NRT-code) | [i] | ||
| 6 | Digital (134, 161, 1070)-net over F2 | [i] | ||