Information on Result #1754289
Digital (167, 186, 173288)-net over F2, using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(2186, 173288, F2, 6, 19) (dual of [(173288, 6), 1039542, 20]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2186, 174767, F2, 6, 19) (dual of [(174767, 6), 1048416, 20]-NRT-code), using
- OOA 6-folding [i] based on linear OA(2186, 1048602, F2, 19) (dual of [1048602, 1048416, 20]-code), using
- 4 times code embedding in larger space [i] based on linear OA(2182, 1048598, F2, 19) (dual of [1048598, 1048416, 20]-code), using
- construction X4 applied to Ce(18) ⊂ Ce(16) [i] based on
- linear OA(2181, 1048576, F2, 19) (dual of [1048576, 1048395, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 220−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(2161, 1048576, F2, 17) (dual of [1048576, 1048415, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 220−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(221, 22, F2, 21) (dual of [22, 1, 22]-code or 22-arc in PG(20,2)), using
- dual of repetition code with length 22 [i]
- linear OA(21, 22, F2, 1) (dual of [22, 21, 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(18) ⊂ Ce(16) [i] based on
- 4 times code embedding in larger space [i] based on linear OA(2182, 1048598, F2, 19) (dual of [1048598, 1048416, 20]-code), using
- OOA 6-folding [i] based on linear OA(2186, 1048602, F2, 19) (dual of [1048602, 1048416, 20]-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.