Information on Result #1712112
Digital (198, 233, 693)-net over F2, using net defined by OOA based on linear OOA(2233, 693, F2, 42, 35) (dual of [(693, 42), 28873, 36]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(2233, 2080, F2, 6, 35) (dual of [(2080, 6), 12247, 36]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2233, 2081, F2, 6, 35) (dual of [(2081, 6), 12253, 36]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2233, 2081, F2, 3, 35) (dual of [(2081, 3), 6010, 36]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2233, 2743, F2, 3, 35) (dual of [(2743, 3), 7996, 36]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(2230, 2742, F2, 3, 35) (dual of [(2742, 3), 7996, 36]-NRT-code), using
- OOA 3-folding [i] based on linear OA(2230, 8226, F2, 35) (dual of [8226, 7996, 36]-code), using
- 2 times code embedding in larger space [i] based on linear OA(2228, 8224, F2, 35) (dual of [8224, 7996, 36]-code), using
- construction X applied to Ce(34) ⊂ Ce(30) [i] based on
- linear OA(2222, 8192, F2, 35) (dual of [8192, 7970, 36]-code), using an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 8191 = 213−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [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(26, 32, F2, 3) (dual of [32, 26, 4]-code or 32-cap in PG(5,2)), using
- construction X applied to Ce(34) ⊂ Ce(30) [i] based on
- 2 times code embedding in larger space [i] based on linear OA(2228, 8224, F2, 35) (dual of [8224, 7996, 36]-code), using
- OOA 3-folding [i] based on linear OA(2230, 8226, F2, 35) (dual of [8226, 7996, 36]-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(2230, 2742, F2, 3, 35) (dual of [(2742, 3), 7996, 36]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2233, 2743, F2, 3, 35) (dual of [(2743, 3), 7996, 36]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2233, 2081, F2, 3, 35) (dual of [(2081, 3), 6010, 36]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2233, 2081, F2, 6, 35) (dual of [(2081, 6), 12253, 36]-NRT-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
None.