Information on Result #808694
Linear OOA(2204, 531, F2, 2, 41) (dual of [(531, 2), 858, 42]-NRT-code), using OOA 2-folding based on linear OA(2204, 1062, F2, 41) (dual of [1062, 858, 42]-code), using
- adding a parity check bit [i] based on linear OA(2203, 1061, F2, 40) (dual of [1061, 858, 41]-code), using
- construction XX applied to C1 = C([1019,34]), C2 = C([1,36]), C3 = C1 + C2 = C([1,34]), and C∩ = C1 ∩ C2 = C([1019,36]) [i] based on
- linear OA(2186, 1023, F2, 39) (dual of [1023, 837, 40]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−4,−3,…,34}, and designed minimum distance d ≥ |I|+1 = 40 [i]
- linear OA(2175, 1023, F2, 36) (dual of [1023, 848, 37]-code), using the primitive narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(2196, 1023, F2, 41) (dual of [1023, 827, 42]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−4,−3,…,36}, and designed minimum distance d ≥ |I|+1 = 42 [i]
- linear OA(2165, 1023, F2, 34) (dual of [1023, 858, 35]-code), using the primitive narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(26, 27, F2, 3) (dual of [27, 21, 4]-code or 27-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
- linear OA(21, 11, F2, 1) (dual of [11, 10, 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 XX applied to C1 = C([1019,34]), C2 = C([1,36]), C3 = C1 + C2 = C([1,34]), and C∩ = C1 ∩ C2 = C([1019,36]) [i] based on
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(2206, 532, F2, 2, 41) (dual of [(532, 2), 858, 42]-NRT-code) | [i] | NRT-Code Embedding in Larger Space | |
| 2 | Linear OOA(2205, 531, F2, 2, 41) (dual of [(531, 2), 857, 42]-NRT-code) | [i] | OOA Duplication | |
| 3 | Linear OOA(2204, 531, F2, 3, 41) (dual of [(531, 3), 1389, 42]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(2204, 531, F2, 4, 41) (dual of [(531, 4), 1920, 42]-NRT-code) | [i] | ||
| 5 | Linear OOA(2204, 531, F2, 5, 41) (dual of [(531, 5), 2451, 42]-NRT-code) | [i] | ||
| 6 | Linear OOA(2204, 531, F2, 6, 41) (dual of [(531, 6), 2982, 42]-NRT-code) | [i] | ||
| 7 | Linear OOA(2204, 531, F2, 7, 41) (dual of [(531, 7), 3513, 42]-NRT-code) | [i] | ||
| 8 | Linear OOA(2204, 531, F2, 8, 41) (dual of [(531, 8), 4044, 42]-NRT-code) | [i] | ||
| 9 | Digital (163, 204, 531)-net over F2 | [i] | ||