Information on Result #1755933
Digital (177, 209, 2051)-net over F2, using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(2209, 2051, F2, 4, 32) (dual of [(2051, 4), 7995, 33]-NRT-code), using
- OOA 4-folding [i] based on linear OA(2209, 8204, F2, 32) (dual of [8204, 7995, 33]-code), using
- discarding factors / shortening the dual code based on linear OA(2209, 8205, F2, 32) (dual of [8205, 7996, 33]-code), using
- 1 times truncation [i] based on linear OA(2210, 8206, F2, 33) (dual of [8206, 7996, 34]-code), using
- construction X applied to Ce(32) ⊂ Ce(30) [i] based on
- linear OA(2209, 8192, F2, 33) (dual of [8192, 7983, 34]-code), using an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 8191 = 213−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(2196, 8192, F2, 31) (dual of [8192, 7996, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 8191 = 213−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(21, 14, F2, 1) (dual of [14, 13, 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 X applied to Ce(32) ⊂ Ce(30) [i] based on
- 1 times truncation [i] based on linear OA(2210, 8206, F2, 33) (dual of [8206, 7996, 34]-code), using
- discarding factors / shortening the dual code based on linear OA(2209, 8205, F2, 32) (dual of [8205, 7996, 33]-code), using
Mode: Linear.
Optimality
Show details for fixed k and m, k and s, k and t, m and s, m and t, t and s.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Digital (178, 210, 2051)-net over F2 | [i] | Net Duplication | |
| 2 | Digital (179, 211, 2051)-net over F2 | [i] | ||