Information on Result #1753209
Digital (149, 169, 13134)-net over F2, using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(2169, 13134, F2, 4, 20) (dual of [(13134, 4), 52367, 21]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2169, 16394, F2, 4, 20) (dual of [(16394, 4), 65407, 21]-NRT-code), using
- 21 times duplication [i] based on linear OOA(2168, 16394, F2, 4, 20) (dual of [(16394, 4), 65408, 21]-NRT-code), using
- OOA 4-folding [i] based on linear OA(2168, 65576, F2, 20) (dual of [65576, 65408, 21]-code), using
- strength reduction [i] based on linear OA(2168, 65576, F2, 21) (dual of [65576, 65408, 22]-code), using
- construction X applied to C([0,10]) ⊂ C([0,8]) [i] based on
- linear OA(2161, 65537, F2, 21) (dual of [65537, 65376, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 232−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- 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(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([0,10]) ⊂ C([0,8]) [i] based on
- strength reduction [i] based on linear OA(2168, 65576, F2, 21) (dual of [65576, 65408, 22]-code), using
- OOA 4-folding [i] based on linear OA(2168, 65576, F2, 20) (dual of [65576, 65408, 21]-code), using
- 21 times duplication [i] based on linear OOA(2168, 16394, F2, 4, 20) (dual of [(16394, 4), 65408, 21]-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.