Information on Result #3179177
Digital (53, 63, 822)-net over F2, using t-expansion based on digital (52, 63, 822)-net over F2, using
- net defined by OOA [i] based on linear OOA(263, 822, F2, 11, 11) (dual of [(822, 11), 8979, 12]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(263, 4111, F2, 11) (dual of [4111, 4048, 12]-code), using
- 1 times code embedding in larger space [i] based on linear OA(262, 4110, F2, 11) (dual of [4110, 4048, 12]-code), using
- construction X4 applied to Ce(10) ⊂ Ce(8) [i] based on
- linear OA(261, 4096, F2, 11) (dual of [4096, 4035, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(249, 4096, F2, 9) (dual of [4096, 4047, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(213, 14, F2, 13) (dual of [14, 1, 14]-code or 14-arc in PG(12,2)), using
- dual of repetition code with length 14 [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 X4 applied to Ce(10) ⊂ Ce(8) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(262, 4110, F2, 11) (dual of [4110, 4048, 12]-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(263, 4111, F2, 11) (dual of [4111, 4048, 12]-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 (54, 64, 822)-net over F2 | [i] | Net Duplication | |