Information on Result #2479825
Linear OOA(2203, 2065, F2, 2, 32) (dual of [(2065, 2), 3927, 33]-NRT-code), using 21 times duplication based on linear OOA(2202, 2065, F2, 2, 32) (dual of [(2065, 2), 3928, 33]-NRT-code), using
- 2 times NRT-code embedding in larger space [i] based on linear OOA(2198, 2063, F2, 2, 32) (dual of [(2063, 2), 3928, 33]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2198, 4126, F2, 32) (dual of [4126, 3928, 33]-code), using
- 1 times truncation [i] based on linear OA(2199, 4127, F2, 33) (dual of [4127, 3928, 34]-code), using
- construction X applied to C([0,16]) ⊂ C([0,14]) [i] based on
- linear OA(2193, 4097, F2, 33) (dual of [4097, 3904, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 224−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
- 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(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([0,16]) ⊂ C([0,14]) [i] based on
- 1 times truncation [i] based on linear OA(2199, 4127, F2, 33) (dual of [4127, 3928, 34]-code), using
- OOA 2-folding [i] based on linear OA(2198, 4126, F2, 32) (dual of [4126, 3928, 33]-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(2203, 1382, F2, 3, 32) (dual of [(1382, 3), 3943, 33]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2203, 1382, F2, 4, 32) (dual of [(1382, 4), 5325, 33]-NRT-code) | [i] | ||
| 3 | Linear OOA(2203, 1382, F2, 5, 32) (dual of [(1382, 5), 6707, 33]-NRT-code) | [i] | ||
| 4 | Linear OOA(2203, 1382, F2, 6, 32) (dual of [(1382, 6), 8089, 33]-NRT-code) | [i] | ||
| 5 | Linear OOA(2203, 1382, F2, 7, 32) (dual of [(1382, 7), 9471, 33]-NRT-code) | [i] | ||
| 6 | Linear OOA(2203, 1382, F2, 8, 32) (dual of [(1382, 8), 10853, 33]-NRT-code) | [i] | ||
| 7 | Digital (171, 203, 1382)-net over F2 | [i] | ||