Information on Result #1749172
Digital (46, 56, 700)-net over F2, using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(256, 700, F2, 2, 10) (dual of [(700, 2), 1344, 11]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(256, 1030, F2, 2, 10) (dual of [(1030, 2), 2004, 11]-NRT-code), using
- OOA 2-folding [i] based on linear OA(256, 2060, F2, 10) (dual of [2060, 2004, 11]-code), using
- 1 times truncation [i] based on linear OA(257, 2061, F2, 11) (dual of [2061, 2004, 12]-code), using
- construction X4 applied to Ce(10) ⊂ Ce(8) [i] based on
- linear OA(256, 2048, F2, 11) (dual of [2048, 1992, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(245, 2048, F2, 9) (dual of [2048, 2003, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(212, 13, F2, 11) (dual of [13, 1, 12]-code), using
- strength reduction [i] based on linear OA(212, 13, F2, 12) (dual of [13, 1, 13]-code or 13-arc in PG(11,2)), using
- dual of repetition code with length 13 [i]
- strength reduction [i] based on linear OA(212, 13, F2, 12) (dual of [13, 1, 13]-code or 13-arc in PG(11,2)), using
- linear OA(21, 13, F2, 1) (dual of [13, 12, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(21, s, F2, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X4 applied to Ce(10) ⊂ Ce(8) [i] based on
- 1 times truncation [i] based on linear OA(257, 2061, F2, 11) (dual of [2061, 2004, 12]-code), using
- OOA 2-folding [i] based on linear OA(256, 2060, F2, 10) (dual of [2060, 2004, 11]-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.