Information on Result #1756393
Digital (189, 215, 11997)-net over F2, using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(2215, 11997, F2, 5, 26) (dual of [(11997, 5), 59770, 27]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2215, 13114, F2, 5, 26) (dual of [(13114, 5), 65355, 27]-NRT-code), using
- OOA 5-folding [i] based on linear OA(2215, 65570, F2, 26) (dual of [65570, 65355, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(2215, 65574, F2, 26) (dual of [65574, 65359, 27]-code), using
- 1 times truncation [i] based on linear OA(2216, 65575, F2, 27) (dual of [65575, 65359, 28]-code), using
- construction X applied to Ce(26) ⊂ Ce(22) [i] based on
- linear OA(2209, 65536, F2, 27) (dual of [65536, 65327, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 65535 = 216−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- 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(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(26) ⊂ Ce(22) [i] based on
- 1 times truncation [i] based on linear OA(2216, 65575, F2, 27) (dual of [65575, 65359, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(2215, 65574, F2, 26) (dual of [65574, 65359, 27]-code), using
- OOA 5-folding [i] based on linear OA(2215, 65570, F2, 26) (dual of [65570, 65355, 27]-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.