Information on Result #1180448
Digital (55, 68, 343)-net over F2, using net defined by OOA based on linear OOA(268, 343, F2, 13, 13) (dual of [(343, 13), 4391, 14]-NRT-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(268, 2059, F2, 13) (dual of [2059, 1991, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(268, 2060, F2, 13) (dual of [2060, 1992, 14]-code), using
- construction X applied to Ce(12) ⊂ Ce(10) [i] based on
- linear OA(267, 2048, F2, 13) (dual of [2048, 1981, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(256, 2048, F2, 11) (dual of [2048, 1992, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(21, 12, F2, 1) (dual of [12, 11, 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(12) ⊂ Ce(10) [i] based on
- discarding factors / shortening the dual code based on linear OA(268, 2060, F2, 13) (dual of [2060, 1992, 14]-code), using
Mode: Constructive and 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 (56, 68, 343)-net over F2 | [i] | t-Expansion | |
| 2 | Digital (56, 69, 343)-net over F2 | [i] | Net Duplication | |
| 3 | Digital (57, 70, 343)-net over F2 | [i] | ||
| 4 | Digital (58, 71, 343)-net over F2 | [i] | ||