Information on Result #2668085
Linear OOA(2180, 1377, F2, 3, 29) (dual of [(1377, 3), 3951, 30]-NRT-code), using 21 times duplication based on linear OOA(2179, 1377, F2, 3, 29) (dual of [(1377, 3), 3952, 30]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(2176, 1376, F2, 3, 29) (dual of [(1376, 3), 3952, 30]-NRT-code), using
- OOA 3-folding [i] based on linear OA(2176, 4128, F2, 29) (dual of [4128, 3952, 30]-code), using
- 1 times code embedding in larger space [i] based on linear OA(2175, 4127, F2, 29) (dual of [4127, 3952, 30]-code), using
- construction X applied to C([0,14]) ⊂ C([0,12]) [i] based on
- linear OA(2169, 4097, F2, 29) (dual of [4097, 3928, 30]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 224−1, defining interval I = [0,14], and minimum distance d ≥ |{−14,−13,…,14}|+1 = 30 (BCH-bound) [i]
- linear OA(2145, 4097, F2, 25) (dual of [4097, 3952, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 224−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(26, 30, F2, 3) (dual of [30, 24, 4]-code or 30-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 C([0,14]) ⊂ C([0,12]) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(2175, 4127, F2, 29) (dual of [4127, 3952, 30]-code), using
- OOA 3-folding [i] based on linear OA(2176, 4128, F2, 29) (dual of [4128, 3952, 30]-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(2180, 1341, F2, 4, 29) (dual of [(1341, 4), 5184, 30]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2180, 1341, F2, 5, 29) (dual of [(1341, 5), 6525, 30]-NRT-code) | [i] | ||
| 3 | Linear OOA(2180, 1341, F2, 6, 29) (dual of [(1341, 6), 7866, 30]-NRT-code) | [i] | ||
| 4 | Linear OOA(2180, 1341, F2, 7, 29) (dual of [(1341, 7), 9207, 30]-NRT-code) | [i] | ||
| 5 | Linear OOA(2180, 1341, F2, 8, 29) (dual of [(1341, 8), 10548, 30]-NRT-code) | [i] | ||
| 6 | Digital (151, 180, 1341)-net over F2 | [i] | ||