Information on Result #1710718
Digital (164, 187, 5981)-net over F2, using net defined by OOA based on linear OOA(2187, 5981, F2, 30, 23) (dual of [(5981, 30), 179243, 24]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(2187, 11963, F2, 6, 23) (dual of [(11963, 6), 71591, 24]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2187, 11963, F2, 5, 23) (dual of [(11963, 5), 59628, 24]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2187, 13115, F2, 5, 23) (dual of [(13115, 5), 65388, 24]-NRT-code), using
- 23 times duplication [i] based on linear OOA(2184, 13115, F2, 5, 23) (dual of [(13115, 5), 65391, 24]-NRT-code), using
- OOA 5-folding [i] based on linear OA(2184, 65575, F2, 23) (dual of [65575, 65391, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(18) [i] based on
- linear OA(2177, 65536, F2, 23) (dual of [65536, 65359, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 65535 = 216−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(2145, 65536, F2, 19) (dual of [65536, 65391, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 65535 = 216−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(27, 39, F2, 3) (dual of [39, 32, 4]-code or 39-cap in PG(6,2)), using
- discarding factors / shortening the dual code based on linear OA(27, 63, F2, 3) (dual of [63, 56, 4]-code or 63-cap in PG(6,2)), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 26−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 4 [i]
- discarding factors / shortening the dual code based on linear OA(27, 63, F2, 3) (dual of [63, 56, 4]-code or 63-cap in PG(6,2)), using
- construction X applied to Ce(22) ⊂ Ce(18) [i] based on
- OOA 5-folding [i] based on linear OA(2184, 65575, F2, 23) (dual of [65575, 65391, 24]-code), using
- 23 times duplication [i] based on linear OOA(2184, 13115, F2, 5, 23) (dual of [(13115, 5), 65391, 24]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2187, 13115, F2, 5, 23) (dual of [(13115, 5), 65388, 24]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2187, 11963, F2, 5, 23) (dual of [(11963, 5), 59628, 24]-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.