Information on Result #1710094
Digital (135, 152, 51729)-net over F2, using net defined by OOA based on linear OOA(2152, 51729, F2, 24, 17) (dual of [(51729, 24), 1241344, 18]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(2152, 51730, F2, 8, 17) (dual of [(51730, 8), 413688, 18]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2152, 51730, F2, 5, 17) (dual of [(51730, 5), 258498, 18]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2152, 52437, F2, 5, 17) (dual of [(52437, 5), 262033, 18]-NRT-code), using
- OOA 5-folding [i] based on linear OA(2152, 262185, F2, 17) (dual of [262185, 262033, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(2152, 262188, F2, 17) (dual of [262188, 262036, 18]-code), using
- construction X applied to C([0,8]) ⊂ C([0,6]) [i] based on
- linear OA(2145, 262145, F2, 17) (dual of [262145, 262000, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 236−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(2109, 262145, F2, 13) (dual of [262145, 262036, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 236−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- linear OA(27, 43, F2, 3) (dual of [43, 36, 4]-code or 43-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 C([0,8]) ⊂ C([0,6]) [i] based on
- discarding factors / shortening the dual code based on linear OA(2152, 262188, F2, 17) (dual of [262188, 262036, 18]-code), using
- OOA 5-folding [i] based on linear OA(2152, 262185, F2, 17) (dual of [262185, 262033, 18]-code), using
- discarding factors / shortening the dual code based on linear OOA(2152, 52437, F2, 5, 17) (dual of [(52437, 5), 262033, 18]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2152, 51730, F2, 5, 17) (dual of [(51730, 5), 258498, 18]-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.