Information on Result #1749416
Digital (61, 71, 5466)-net over F2, using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(271, 5466, F2, 3, 10) (dual of [(5466, 3), 16327, 11]-NRT-code), using
- OOA 3-folding [i] based on linear OA(271, 16398, F2, 10) (dual of [16398, 16327, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(271, 16399, F2, 10) (dual of [16399, 16328, 11]-code), using
- 1 times truncation [i] based on linear OA(272, 16400, F2, 11) (dual of [16400, 16328, 12]-code), using
- construction X4 applied to Ce(10) ⊂ Ce(8) [i] based on
- linear OA(271, 16384, F2, 11) (dual of [16384, 16313, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 16383 = 214−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(257, 16384, F2, 9) (dual of [16384, 16327, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 16383 = 214−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(215, 16, F2, 15) (dual of [16, 1, 16]-code or 16-arc in PG(14,2)), using
- dual of repetition code with length 16 [i]
- linear OA(21, 16, F2, 1) (dual of [16, 15, 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(10) ⊂ Ce(8) [i] based on
- 1 times truncation [i] based on linear OA(272, 16400, F2, 11) (dual of [16400, 16328, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(271, 16399, F2, 10) (dual of [16399, 16328, 11]-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 (62, 72, 5466)-net over F2 | [i] | Net Duplication | |