Information on Result #1711146
Digital (166, 193, 1729)-net over F2, using net defined by OOA based on linear OOA(2193, 1729, F2, 35, 27) (dual of [(1729, 35), 60322, 28]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(2193, 3459, F2, 7, 27) (dual of [(3459, 7), 24020, 28]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2193, 3459, F2, 4, 27) (dual of [(3459, 4), 13643, 28]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2193, 4105, F2, 4, 27) (dual of [(4105, 4), 16227, 28]-NRT-code), using
- 22 times duplication [i] based on linear OOA(2191, 4105, F2, 4, 27) (dual of [(4105, 4), 16229, 28]-NRT-code), using
- OOA 4-folding [i] based on linear OA(2191, 16420, F2, 27) (dual of [16420, 16229, 28]-code), using
- 1 times code embedding in larger space [i] based on linear OA(2190, 16419, F2, 27) (dual of [16419, 16229, 28]-code), using
- construction X applied to Ce(26) ⊂ Ce(22) [i] based on
- linear OA(2183, 16384, F2, 27) (dual of [16384, 16201, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 16383 = 214−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(2155, 16384, F2, 23) (dual of [16384, 16229, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 16383 = 214−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(27, 35, F2, 3) (dual of [35, 28, 4]-code or 35-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 code embedding in larger space [i] based on linear OA(2190, 16419, F2, 27) (dual of [16419, 16229, 28]-code), using
- OOA 4-folding [i] based on linear OA(2191, 16420, F2, 27) (dual of [16420, 16229, 28]-code), using
- 22 times duplication [i] based on linear OOA(2191, 4105, F2, 4, 27) (dual of [(4105, 4), 16229, 28]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2193, 4105, F2, 4, 27) (dual of [(4105, 4), 16227, 28]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2193, 3459, F2, 4, 27) (dual of [(3459, 4), 13643, 28]-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.