Information on Result #1131708
Linear OOA(2158, 21849, F2, 6, 19) (dual of [(21849, 6), 130936, 20]-NRT-code), using OOA 6-folding based on linear OA(2158, 131094, F2, 19) (dual of [131094, 130936, 20]-code), using
- 2 times code embedding in larger space [i] based on linear OA(2156, 131092, F2, 19) (dual of [131092, 130936, 20]-code), using
- adding a parity check bit [i] based on linear OA(2155, 131091, F2, 18) (dual of [131091, 130936, 19]-code), using
- construction X4 applied to C([0,18]) ⊂ C([1,16]) [i] based on
- linear OA(2154, 131071, F2, 19) (dual of [131071, 130917, 20]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 131071 = 217−1, defining interval I = [0,18], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(2136, 131071, F2, 16) (dual of [131071, 130935, 17]-code), using the primitive narrow-sense BCH-code C(I) with length 131071 = 217−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(219, 20, F2, 19) (dual of [20, 1, 20]-code or 20-arc in PG(18,2)), using
- dual of repetition code with length 20 [i]
- linear OA(21, 20, F2, 1) (dual of [20, 19, 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 X4 applied to C([0,18]) ⊂ C([1,16]) [i] based on
- adding a parity check bit [i] based on linear OA(2155, 131091, F2, 18) (dual of [131091, 130936, 19]-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, 21849, F2, 6, 19) (dual of [(21849, 6), 130935, 20]-NRT-code) | [i] | OOA Duplication | |
| 2 | Linear OOA(2157, 21848, F2, 6, 18) (dual of [(21848, 6), 130931, 19]-NRT-code) | [i] | Truncation for OOAs | |
| 3 | Linear OOA(2158, 21849, F2, 7, 19) (dual of [(21849, 7), 152785, 20]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(2158, 21849, F2, 8, 19) (dual of [(21849, 8), 174634, 20]-NRT-code) | [i] | ||
| 5 | Digital (139, 158, 21849)-net over F2 | [i] | ||