Information on Result #2480307
Linear OOA(2219, 1039, F2, 2, 38) (dual of [(1039, 2), 1859, 39]-NRT-code), using 21 times duplication based on linear OOA(2218, 1039, F2, 2, 38) (dual of [(1039, 2), 1860, 39]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(2216, 1038, F2, 2, 38) (dual of [(1038, 2), 1860, 39]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2216, 2076, F2, 38) (dual of [2076, 1860, 39]-code), using
- strength reduction [i] based on linear OA(2216, 2076, F2, 39) (dual of [2076, 1860, 40]-code), using
- construction X applied to Ce(38) ⊂ Ce(34) [i] based on
- linear OA(2210, 2048, F2, 39) (dual of [2048, 1838, 40]-code), using an extension Ce(38) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,38], and designed minimum distance d ≥ |I|+1 = 39 [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(26, 28, F2, 3) (dual of [28, 22, 4]-code or 28-cap in PG(5,2)), using
- discarding factors / shortening the dual code based on linear OA(26, 32, F2, 3) (dual of [32, 26, 4]-code or 32-cap in PG(5,2)), using
- construction X applied to Ce(38) ⊂ Ce(34) [i] based on
- strength reduction [i] based on linear OA(2216, 2076, F2, 39) (dual of [2076, 1860, 40]-code), using
- OOA 2-folding [i] based on linear OA(2216, 2076, F2, 38) (dual of [2076, 1860, 39]-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(2219, 972, F2, 3, 38) (dual of [(972, 3), 2697, 39]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2219, 972, F2, 4, 38) (dual of [(972, 4), 3669, 39]-NRT-code) | [i] | ||
| 3 | Linear OOA(2219, 972, F2, 5, 38) (dual of [(972, 5), 4641, 39]-NRT-code) | [i] | ||
| 4 | Linear OOA(2219, 972, F2, 6, 38) (dual of [(972, 6), 5613, 39]-NRT-code) | [i] | ||
| 5 | Linear OOA(2219, 972, F2, 7, 38) (dual of [(972, 7), 6585, 39]-NRT-code) | [i] | ||
| 6 | Linear OOA(2219, 972, F2, 8, 38) (dual of [(972, 8), 7557, 39]-NRT-code) | [i] | ||
| 7 | Digital (181, 219, 972)-net over F2 | [i] | ||