Information on Result #1616128
Linear OOA(2252, 2097833, F2, 4, 18) (dual of [(2097833, 4), 8391080, 19]-NRT-code), using (u, u+v)-construction based on
- linear OOA(245, 683, F2, 4, 9) (dual of [(683, 4), 2687, 10]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(245, 683, F2, 3, 9) (dual of [(683, 3), 2004, 10]-NRT-code), using
- OOA 3-folding [i] based on linear OA(245, 2049, F2, 9) (dual of [2049, 2004, 10]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 2049 | 222−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- OOA 3-folding [i] based on linear OA(245, 2049, F2, 9) (dual of [2049, 2004, 10]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(245, 683, F2, 3, 9) (dual of [(683, 3), 2004, 10]-NRT-code), using
- linear OOA(2207, 2097150, F2, 4, 18) (dual of [(2097150, 4), 8388393, 19]-NRT-code), using
- OOA 4-folding [i] based on linear OA(2207, 8388600, F2, 18) (dual of [8388600, 8388393, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(2207, large, F2, 18) (dual of [large, large−207, 19]-code), using
- the primitive narrow-sense BCH-code C(I) with length 8388607 = 223−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- discarding factors / shortening the dual code based on linear OA(2207, large, F2, 18) (dual of [large, large−207, 19]-code), using
- OOA 4-folding [i] based on linear OA(2207, 8388600, F2, 18) (dual of [8388600, 8388393, 19]-code), using
Mode: Linear.
Optimality
Show details for fixed k and m, k and s, k and t, m and s, m 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(2252, 2097833, F2, 5, 18) (dual of [(2097833, 5), 10488913, 19]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2252, 2097833, F2, 6, 18) (dual of [(2097833, 6), 12586746, 19]-NRT-code) | [i] | ||
| 3 | Linear OOA(2252, 2097833, F2, 7, 18) (dual of [(2097833, 7), 14684579, 19]-NRT-code) | [i] | ||
| 4 | Linear OOA(2252, 2097833, F2, 8, 18) (dual of [(2097833, 8), 16782412, 19]-NRT-code) | [i] | ||
| 5 | Digital (234, 252, 2097833)-net over F2 | [i] | ||