Information on Result #1709718
Digital (119, 135, 16392)-net over F2, using net defined by OOA based on linear OOA(2135, 16392, F2, 24, 16) (dual of [(16392, 24), 393273, 17]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(2135, 16393, F2, 8, 16) (dual of [(16393, 8), 131009, 17]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2135, 16393, F2, 4, 16) (dual of [(16393, 4), 65437, 17]-NRT-code), using
- OOA 4-folding [i] based on linear OA(2135, 65572, F2, 16) (dual of [65572, 65437, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(2135, 65575, F2, 16) (dual of [65575, 65440, 17]-code), using
- 1 times truncation [i] based on linear OA(2136, 65576, F2, 17) (dual of [65576, 65440, 18]-code), using
- construction X applied to C([0,8]) ⊂ C([0,6]) [i] based on
- linear OA(2129, 65537, F2, 17) (dual of [65537, 65408, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 232−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(297, 65537, F2, 13) (dual of [65537, 65440, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 232−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [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 C([0,8]) ⊂ C([0,6]) [i] based on
- 1 times truncation [i] based on linear OA(2136, 65576, F2, 17) (dual of [65576, 65440, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(2135, 65575, F2, 16) (dual of [65575, 65440, 17]-code), using
- OOA 4-folding [i] based on linear OA(2135, 65572, F2, 16) (dual of [65572, 65437, 17]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2135, 16393, F2, 4, 16) (dual of [(16393, 4), 65437, 17]-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.