Information on Result #2667077
Linear OOA(2122, 2736, F2, 3, 18) (dual of [(2736, 3), 8086, 19]-NRT-code), using 21 times duplication based on linear OOA(2121, 2736, F2, 3, 18) (dual of [(2736, 3), 8087, 19]-NRT-code), using
- strength reduction [i] based on linear OOA(2121, 2736, F2, 3, 19) (dual of [(2736, 3), 8087, 20]-NRT-code), using
- OOA 3-folding [i] based on linear OA(2121, 8208, F2, 19) (dual of [8208, 8087, 20]-code), using
- 2 times code embedding in larger space [i] based on linear OA(2119, 8206, F2, 19) (dual of [8206, 8087, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(16) [i] based on
- linear OA(2118, 8192, F2, 19) (dual of [8192, 8074, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 8191 = 213−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(2105, 8192, F2, 17) (dual of [8192, 8087, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 8191 = 213−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [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(18) ⊂ Ce(16) [i] based on
- 2 times code embedding in larger space [i] based on linear OA(2119, 8206, F2, 19) (dual of [8206, 8087, 20]-code), using
- OOA 3-folding [i] based on linear OA(2121, 8208, F2, 19) (dual of [8208, 8087, 20]-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(2122, 2169, F2, 4, 18) (dual of [(2169, 4), 8554, 19]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2122, 2169, F2, 5, 18) (dual of [(2169, 5), 10723, 19]-NRT-code) | [i] | ||
| 3 | Linear OOA(2122, 2169, F2, 6, 18) (dual of [(2169, 6), 12892, 19]-NRT-code) | [i] | ||
| 4 | Linear OOA(2122, 2169, F2, 7, 18) (dual of [(2169, 7), 15061, 19]-NRT-code) | [i] | ||
| 5 | Linear OOA(2122, 2169, F2, 8, 18) (dual of [(2169, 8), 17230, 19]-NRT-code) | [i] | ||
| 6 | Digital (104, 122, 2169)-net over F2 | [i] | ||