Information on Result #2788871
Linear OOA(2169, 16394, F2, 4, 20) (dual of [(16394, 4), 65407, 21]-NRT-code), using 21 times duplication based on linear OOA(2168, 16394, F2, 4, 20) (dual of [(16394, 4), 65408, 21]-NRT-code), using
- OOA 4-folding [i] based on linear OA(2168, 65576, F2, 20) (dual of [65576, 65408, 21]-code), using
- strength reduction [i] based on linear OA(2168, 65576, F2, 21) (dual of [65576, 65408, 22]-code), using
- construction X applied to C([0,10]) ⊂ C([0,8]) [i] based on
- linear OA(2161, 65537, F2, 21) (dual of [65537, 65376, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 232−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(2129, 65537, F2, 17) (dual of [65537, 65408, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 232−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(27, 39, F2, 3) (dual of [39, 32, 4]-code or 39-cap in PG(6,2)), using
- discarding factors / shortening the dual code based on linear OA(27, 63, F2, 3) (dual of [63, 56, 4]-code or 63-cap in PG(6,2)), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 26−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 4 [i]
- discarding factors / shortening the dual code based on linear OA(27, 63, F2, 3) (dual of [63, 56, 4]-code or 63-cap in PG(6,2)), using
- construction X applied to C([0,10]) ⊂ C([0,8]) [i] based on
- strength reduction [i] based on linear OA(2168, 65576, F2, 21) (dual of [65576, 65408, 22]-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(2169, 13134, F2, 5, 20) (dual of [(13134, 5), 65501, 21]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2169, 13134, F2, 6, 20) (dual of [(13134, 6), 78635, 21]-NRT-code) | [i] | ||
| 3 | Linear OOA(2169, 13134, F2, 7, 20) (dual of [(13134, 7), 91769, 21]-NRT-code) | [i] | ||
| 4 | Linear OOA(2169, 13134, F2, 8, 20) (dual of [(13134, 8), 104903, 21]-NRT-code) | [i] | ||
| 5 | Digital (149, 169, 13134)-net over F2 | [i] | ||