Information on Result #1095625
Linear OOA(2159, 104866, F2, 5, 16) (dual of [(104866, 5), 524171, 17]-NRT-code), using OOA 5-folding based on linear OA(2159, 524330, F2, 16) (dual of [524330, 524171, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(2159, 524333, F2, 16) (dual of [524333, 524174, 17]-code), using
- 1 times truncation [i] based on linear OA(2160, 524334, F2, 17) (dual of [524334, 524174, 18]-code), using
- construction X applied to C([0,8]) ⊂ C([0,6]) [i] based on
- linear OA(2153, 524289, F2, 17) (dual of [524289, 524136, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 524289 | 238−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(2115, 524289, F2, 13) (dual of [524289, 524174, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 524289 | 238−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- linear OA(27, 45, F2, 3) (dual of [45, 38, 4]-code or 45-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([0,8]) ⊂ C([0,6]) [i] based on
- 1 times truncation [i] based on linear OA(2160, 524334, F2, 17) (dual of [524334, 524174, 18]-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(2159, 104866, F2, 6, 16) (dual of [(104866, 6), 629037, 17]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2159, 104866, F2, 7, 16) (dual of [(104866, 7), 733903, 17]-NRT-code) | [i] | ||
| 3 | Linear OOA(2159, 104866, F2, 8, 16) (dual of [(104866, 8), 838769, 17]-NRT-code) | [i] | ||
| 4 | Digital (143, 159, 104866)-net over F2 | [i] | ||