Information on Result #2865154
Linear OOA(2176, 104862, F2, 5, 18) (dual of [(104862, 5), 524134, 19]-NRT-code), using 22 times duplication based on linear OOA(2174, 104862, F2, 5, 18) (dual of [(104862, 5), 524136, 19]-NRT-code), using
- OOA 5-folding [i] based on linear OA(2174, 524310, F2, 18) (dual of [524310, 524136, 19]-code), using
- 2 times code embedding in larger space [i] based on linear OA(2172, 524308, F2, 18) (dual of [524308, 524136, 19]-code), using
- 1 times truncation [i] based on linear OA(2173, 524309, F2, 19) (dual of [524309, 524136, 20]-code), using
- construction X4 applied to Ce(18) ⊂ Ce(16) [i] based on
- linear OA(2172, 524288, F2, 19) (dual of [524288, 524116, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 524287 = 219−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(2153, 524288, F2, 17) (dual of [524288, 524135, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 524287 = 219−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(220, 21, F2, 19) (dual of [21, 1, 20]-code), using
- strength reduction [i] based on linear OA(220, 21, F2, 20) (dual of [21, 1, 21]-code or 21-arc in PG(19,2)), using
- dual of repetition code with length 21 [i]
- strength reduction [i] based on linear OA(220, 21, F2, 20) (dual of [21, 1, 21]-code or 21-arc in PG(19,2)), using
- linear OA(21, 21, F2, 1) (dual of [21, 20, 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 Ce(18) ⊂ Ce(16) [i] based on
- 1 times truncation [i] based on linear OA(2173, 524309, F2, 19) (dual of [524309, 524136, 20]-code), using
- 2 times code embedding in larger space [i] based on linear OA(2172, 524308, F2, 18) (dual of [524308, 524136, 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(2176, 103031, F2, 6, 18) (dual of [(103031, 6), 618010, 19]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2176, 103031, F2, 7, 18) (dual of [(103031, 7), 721041, 19]-NRT-code) | [i] | ||
| 3 | Linear OOA(2176, 103031, F2, 8, 18) (dual of [(103031, 8), 824072, 19]-NRT-code) | [i] | ||
| 4 | Digital (158, 176, 103031)-net over F2 | [i] | ||